Výsledky

Krácení
Sčítání a odčítání
Násobení
Dělení
Složené lomené výrazy

Krácení:

1) $\displaystyle a)\ \frac{a}{b}, b\ne 0;\ b)\ \frac{u}{{{v}^{2}}}, v\ne 0;\ c)\ \frac{p}{{{q}^{3}}}, q\ne 0;\ d)\ \frac{4}{7}, x\ne 0;$ $\displaystyle e)\ \frac{{{r}^{2}}}{2s}, s\ne 0;\ f)\ \frac{2m}{3{{n}^{2}}}, n\ne 0;\ g)\ \frac{x}{y}, a\ne 0, y\ne 0;\ h)\ \frac{2}{5}, z\ne 0;$

2) $\displaystyle a)\ \frac{1}{{{x}^{2}}}, x\ne 0;\ b)\ \frac{2{{c}^{3}}}{5}, c\ne 0;\ c)\ \frac{k}{2}, k\ne 0;\ d)\ \frac{2{{s}^{2}}}{5}, s\ne 0$ $\displaystyle e)\ \frac{1}{4a}, a\ne 0, b\ne 0;\ f)\ 5m, m\ne 0;\ g)\ \frac{r}{x}, r\ne 0, x\ne 0;\ h)\ \frac{7}{{{u}^{2}}}, u\ne 0;$

3) $\displaystyle a)\ \frac{1}{ab}, a\ne 0, b\ne 0;\ b)\ \frac{5u}{7v}, u\ne 0, v\ne 0;\ c)\ \frac{4y}{5xz}, x\ne 0, z\ne 0;$

$\displaystyle d)\ \frac{v}{5u},u\ne 0,\ v\ne 0;\ e)\ \frac{2}{3{{p}^{3}}q},p\ne 0,\,q\ne 0;\ f)\frac{4{{a}^{2}}}{5},a\ne 0,\,x\ne 0;$

$\displaystyle g)\ \frac{b}{4ac}, a\ne 0, b\ne 0, c\ne 0;\ h)\ \frac{15r}{17}, r\ne 0, s\ne 0;$

4) $\displaystyle a)\ \frac{1}{{{m}^{2}}n}, k\ne 0, m\ne 0, n\ne 0;\ b)\ \frac{{{c}^{2}}}{3{{d}^{3}}}, b\ne 0, d\ne 0;\ c)\ r, r\ne 0, s\ne 0;$ $\displaystyle d)\ \frac{x}{y}, x\ne 0, y\ne 0;\ e)\ \frac{2a}{9{{b}^{2}}}, a\ne 0, b\ne 0;\ f)\ \frac{3}{{{n}^{2}}}, m\ne 0, n\ne 0;$ $\displaystyle g)\ 4, u\ne 0;\ h)\ \frac{1}{{{q}^{2}}}, p\ne 0, q\ne 0, r\ne 0;$

5) $\displaystyle a)\ \frac{u}{v}, v\ne 0, x\ne 1;\ b)\ \frac{1}{5}, x\ne 2;\ c)\ \frac{3}{7}, a\ne -b;\ d)\ \frac{4}{r}, r\ne 0, q\ne -3p;$ $\displaystyle e)\ \frac{5}{3}, m\ne -2n;\ f)\ 4, r\ne \pm 1;\ g)\ \frac{2}{x}, x\ne 0, x\ne y;\ h)\ \frac{1}{2}, a\ne 2;$

6) $\displaystyle a)\ \frac{1}{k}, k\ne 0, k\ne -1;\ b)\ 3r, r\ne 0, r\ne 1;\ c)\ \frac{m+1}{m-1}, m\ne 0, m\ne 1;$ $\displaystyle d)\ \frac{b}{a}, a\ne 0, a\ne 4b;\ e)\ \frac{r}{2}, s\ne \frac{7}{5}t;\ f)\ \frac{9}{z}, z\ne 0, v\ne \frac{{{z}^{2}}}{3};$ $\displaystyle g)\ \frac{2\left( x+1 \right)}{y+1}, x\ne 0,y\ne -1;\ h)\ \frac{b+3}{a-2}, a\ne 0, a\ne 2;\ i)\ \frac{2\left( x-y \right)}{3y}, x\ne y, y\ne 0;$

7) $\displaystyle a)\ \frac{1}{a-b}, a\ne \pm b;\ b)\ r-2, r\ne -2;\ c)\ \frac{1}{a+x}, x\ne -a;$ $\displaystyle d)\ \frac{1}{u-3}, u\ne \pm 3;\ e)\ \frac{m+n}{n}, n\ne 0, m\ne -n;\ f)\ 1, s\ne \pm 4;$ $\displaystyle g)\ \frac{z-1}{a}, a\ne 0, z\ne -1;\ h)\ \frac{x}{x-5}, x\ne \pm 5;\ i)\ \frac{1}{r+s}, r\ne -s;$

8) $\displaystyle a)\ \frac{3}{p-q}, p\ne q; b)\ \frac{a+1}{2}, a\ne -1;\ c)\ \frac{1}{h+1}, h\ne \pm 1;$ $\displaystyle d)\ \frac{h+3}{2k}, h\ne 0, k\ne 0;\ e)\ 2+p, p\ne 0, q\ne 0;\ f)\ \frac{a-c}{abc}, a\ne 0, b\ne 0, c\ne 0;$ $\displaystyle g)\ \frac{y}{x-{{y}^{2}}}, x\ne 0, y\ne 0, x\ne {{y}^{2}};\ h)\ \frac{{{u}^{2}}+v}{{{u}^{3}}}, u\ne 0; i)\ \frac{7}{4\left( a-2 \right)}, a\ne \pm 2$

9) $\displaystyle a)\ \frac{3+5b}{2a}, a\ne 0, b\ne 0; b)\ \frac{2x-1}{{{x}^{2}}}, x\ne 0, y\ne 0; c)\ \frac{1}{5-m}, m\ne \pm 5;$ $\displaystyle d)\ \frac{x-1}{x+1}, x\ne 0, x\ne -1;\ e)\ \frac{5}{c-2}, a\ne 0, b\ne 0, c\ne 2;\ f)\ {{s}^{2}}-5, s\ne 0, r\ne 0;$ $\displaystyle g)\ \frac{1}{a}, a\ne 0, x\ne -1;\ h)\ -\frac{a}{b}, b\ne 0, a\ne b;\ i)\ \frac{9a}{{{a}^{2}}-4}, a\ne \pm 2;$

Sčítání a odčítání:

1) $\displaystyle a)\ \frac{9u}{8};\$ $\displaystyle b)\ \frac{c+2}{y}, y\ne 0;\$ $\displaystyle c)\ \frac{4ab}{5};\$ $\displaystyle d)\ \frac{2}{p}, p\ne 0;$ $\displaystyle e)\ 2, y\ne 0;\$ $\displaystyle f) \frac{1}{d}, d\ne 0;$

2) $\displaystyle a)\ \frac{10+m}{5};\$ $\displaystyle b)\ \frac{2r}{3};\$ $\displaystyle c)\ \frac{1+2a}{2};$ $\displaystyle d)\ \frac{a-b}{b}, b\ne 0;\$ $\displaystyle e)\ -\frac{4x}{5};\$ $\displaystyle f)\ \frac{3y}{4};\$ $\displaystyle g)\ \frac{3v-u}{v}, v\ne 0;\$ $\displaystyle h)\ \frac{ab+a}{b}, b\ne 0;\$ $\displaystyle i)\ \frac{1-{{s}^{2}}}{s}, s\ne 0;$

3) $\displaystyle a)\ \frac{3a}{4};\$ $\displaystyle b)\ \frac{4x+3y+2z}{12};\$ $\displaystyle c)\ \frac{11r}{18};\$ $\displaystyle d)\ 3x;\$ $\displaystyle e)\ \frac{a}{15};\$ $\displaystyle f)\ \frac{a\left( a-5 \right)}{30};\$ $\displaystyle g)\ \frac{{{z}^{2}}}{10};\$ $\displaystyle h)\ \frac{y-30x}{20};\$ $\displaystyle i)\ \frac{26s+21}{21};$

4) $\displaystyle a)\ \frac{5a+2b}{9b}, a\ne 0, b\ne 0;\ b)\ \frac{n}{6a}, a\ne 0;\$ $\displaystyle c)\ \frac{3x}{b}, b\ne 0;\ d)\ \frac{11s}{12x},x\ne 0;\$ $\displaystyle e)\ \frac{z}{10},z\ne 0;\ f)\ \frac{4a+3b}{24t}, t\ne 0;$

5) $\displaystyle a)\ \frac{4x+3y}{4y}, y\ne 0;\ b)\ \frac{3}{10m}, m\ne 0;\$ $\displaystyle c)\ \frac{h-10}{5h}, h\ne 0;\ d)\ \frac{2a+b}{4x}, x\ne 0;\$ $\displaystyle e)\ \frac{2{{x}^{2}}-3{{y}^{2}}}{3xy}, x\ne 0, y\ne 0;\ f)\ \frac{39c}{20d}, d\ne 0;$

6) $\displaystyle a)\ \frac{3m-n}{6};\ b)\ \frac{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}{abc}, a\ne 0, b\ne 0, c\ne 0;\$ $\displaystyle c)\ \frac{{{\left( r+s \right)}^{2}}}{{{r}^{4}}}, r\ne 0;\ d)\ \frac{4}{x}, x\ne 0;\$ $\displaystyle e)\ \frac{5r}{12s},s\ne 0;\ f)\ \frac{yz+xz+xy}{xyz},x\ne 0,y\ne 0,z\ne 0;$

7) $\displaystyle a)\ \frac{17}{30ab}, a\ne 0, b\ne 0;\ b)\ \frac{4ut-3vs}{24st}, s\ne 0, t\ne 0;\$ $\displaystyle c)\ \frac{a}{20b}, b\ne 0;\ d)\ \frac{3p}{5q}, q\ne 0;\$ $\displaystyle e)\ \frac{3x+2y}{36y}, y\ne 0;\ f)\ \frac{\left( c-b \right)\left( c+b \right)}{abc}, a\ne 0, b\ne 0, c\ne 0;$

8) $\displaystyle a)\ \frac{{{y}^{2}}+2x+4y}{2y}; y\ne 0;\ b)\ \frac{a+b+ab}{b}; b\ne 0;$ $\displaystyle c)\ \frac{x+1}{4};\ d)\ \frac{3v}{8};\ e)\ \frac{7z-3}{6};\ f)\ \frac{26a+3}{12};\$ $\displaystyle g)\ \frac{8x+11y}{30};\ h)\ \frac{6p-11q}{36};\ i)\ \frac{{{\left( x-y \right)}^{2}}}{{{y}^{2}}}; y\ne 0;\$ $\displaystyle j)\ 4; a\ne 0;\ k)\ \frac{2n-1}{15};\ l)\ \frac{a+3b}{24};\ m)\ \frac{27r+4s}{12};\$ $\displaystyle n)\ \frac{ab}{21};\ o)\ \frac{17{{s}^{2}}-33{{r}^{2}}}{20};\ p)\ \frac{-4m-3n}{24};$

9) $\displaystyle a)\ \frac{xc+xb}{abc};\ a\ne 0, b\ne 0, c\ne 0;\ b)\ \frac{5r}{2p}; p\ne 0; c)\ \frac{{{\left( a+b \right)}^{2}}}{ab}; a\ne 0, b\ne 0;\$ $\displaystyle d)\ \frac{{{x}^{2}}+xy+{{y}^{2}}}{xy}; x\ne 0, y\ne 0;\ e)\ \frac{b+a}{abx}; a\ne 0, b\ne 0, x\ne 0;\$ $\displaystyle f)\ \frac{3u-4v-28}{14v}; v\ne 0;$

10) $\displaystyle a)\ \frac{11a+23b}{12};\ b)\ \frac{5n-7}{12};\ c)\ \frac{2r-5s+33}{30};\ d)\ \frac{22x+101y}{24};$

11) $\displaystyle a)\ \frac{2a-3{{x}^{2}}}{{{x}^{3}}};\ x\ne 0;\ b)\ \frac{{{c}^{4}}+{{d}^{3}}}{{{c}^{3}}{{d}^{2}}};\ c\ne 0,\,d\ne 0;\ c)\ \frac{2x+y}{{{x}^{4}}{{y}^{4}}};\ x\ne 0,\,y\ne 0;\$ $\displaystyle d)\ \frac{3{{a}^{2}}-4b}{{{a}^{4}}{{b}^{3}}};\ a\ne 0,\,b\ne 0;\ e)\ \frac{3ax-2b}{6{{x}^{2}}};\ x\ne 0;\$ $\displaystyle f)\ \frac{9bx+30ax-2b}{12{{a}^{2}}{{b}^{2}}};\ a\ne 0,\,b\ne 0;\ g)\ \frac{30tuv+4vz-7}{6{{u}^{2}}{{v}^{2}}};\ u\ne 0,\,v\ne 0;\$ $\displaystyle h)\ \frac{7ab-4{{a}^{2}}-3{{b}^{2}}}{{{a}^{2}}{{b}^{2}}};\ a\ne 0,\,b\ne 0;\ i)\ \frac{5{{r}^{2}}s+6r-5{{s}^{2}}}{{{r}^{2}}{{s}^{2}}};\ r\ne 0,\,s\ne 0;\$ $\displaystyle j)\ \frac{6{{a}^{2}}+2a-5}{{{a}^{2}}b};\ a\ne 0,\,b\ne 0;\ k)\ \frac{2{{x}^{2}}-1}{{{x}^{2}}y};\ x\ne 0,\,y\ne 0;\$

12) $\displaystyle a)\ \frac{y\left( {x}^{2}-1 \right)}{x};\ x\ne 0;\ b)\ \frac{-2a+4b}{3};\ c)\ \frac{2x}{a-b};\ a\ne b;\$ $\displaystyle d)\ \frac{3}{x+y};\ x\ne -y;\ e)\ \frac{2m-7}{n+2};\ n\ne -2;\ f)\ \frac{x}{a-b};\ a\ne b;\$ $\displaystyle g)\ \frac{u+v}{y-1};\ y\ne 1;\ h)\ \frac{5m-1}{6};\ i)\ \frac{3\left( u-v \right)}{4};\ j)\ \frac{a-2}{5v+z};\ z\ne -5v;\$ $\displaystyle k)\ \frac{r+5}{r+s};\ r\ne -s;\ l)\ \frac{8z-15}{v\left( u-v \right)};\ v\ne 0,\,u\ne v;\ m)\ \frac{1}{r-3};\ r\ne 3;\$ $\displaystyle n)\ \frac{7{{a}^{2}}}{b-2};\ b\ne 2;\ o)\ \frac{3}{a-1};\ a\ne 1;\ p)\ \frac{m-n}{2p-q};\ q\ne 2p;\$ $\displaystyle q)\ \frac{r+20}{s+5{{r}^{2}}};\ s\ne -5{{r}^{2}};\ r)\ \frac{a+b}{{{x}^{2}}-1};\ x\ne \pm 1;\ s)\ \frac{-10}{a-3};\ a\ne 3;\$ $\displaystyle t)\ \frac{-1}{u-v};\ u\ne v;\ u)\ \frac{c+4}{a-b};\ a\ne b;\ v)\ \frac{a+b+c}{x-y};\ x\ne y;$

13) $\displaystyle a)\ \frac{a}{a-1};\ a\ne 1,\ b)\ \frac{1-x}{x+1};\ x\ne -1,\ c)\ \frac{-y}{y+1};\ y\ne -1,\ d)\ \frac{{{t}^{2}}}{t-s};\ t\ne s,\$ $\displaystyle e)\ \frac{1-p}{p+1};\ p\ne -1,\ f)\ \frac{-2z}{z+1};\ z\ne -1,\ g)\ \frac{6}{a+2};\ a\ne -2,\ h)\ \frac{-2r}{r+s};\ r\ne -s,$ $\displaystyle i)\ \frac{c+5d}{c-2d};\ c\ne 2d,\ j)\ \frac{-8r}{r+s};\ r\ne -s,\ k)\ \frac{a+10}{2b+5};\ b\ne -2,5,$ $\displaystyle l)\ \frac{11}{3\left( x+y \right)};\ x\ne -y,\ m)\ \frac{3m}{2\left( m-1 \right)};\ m\ne 1,\ n)\ \frac{9a-4}{4\left( a+2 \right)};\ a\ne -2,$ $\displaystyle o)\ \frac{{{x}^{2}}+{{y}^{2}}}{x\left( 1-y \right)};\ x\ne 0,\ y\ne 1,\ p)\ \frac{a}{6\left( a+b \right)};\ a\ne -b,\ q)\ \frac{3r+2}{10\left( p-3 \right)};\ p\ne 3$

14) $\displaystyle a)\ \frac{15}{4\left( x+1 \right)};\ x\ne -1,\ b)\ \frac{3}{10\left( a-1 \right)};\ a\ne 1,\ c)\ 0;\ a\ne -b,$ $\displaystyle d)\ \frac{2x}{\left( x-y \right)\left( x+y \right)};\ x\ne \pm y,\ e)\ \frac{2b}{\left( a-b \right)\left( a+b \right)};\ a\ne \pm b,$ $\displaystyle f)\ \frac{4r}{\left( 2r-s \right)\left( 2r+s \right)};\ s\ne \pm 2r,\ g)\ \frac{1}{y\left( y-1 \right)};\ y\ne 0,\ y\ne 1,\$ $\displaystyle h)\ \frac{5x}{8\left( x+y \right)};\ x\ne -y,\ i)\ \frac{2a+ac+c}{2c\left( a-b \right)};\ c\ne 0,\ a\ne b,\$ $\displaystyle j)\ \frac{5m-n}{{{m}^{2}}-{{n}^{2}}};\ m\ne \pm n,\ k)\ \frac{20}{{{v}^{2}}-4};\ v\ne \pm 2,\ l)\ \frac{2p+6q}{{{p}^{2}}-{{q}^{2}}};p\ \ne \pm q,\$ $\displaystyle m)\ \frac{4p}{{{q}^{2}}-4};\ q\ne \pm 2,\ n)\ \frac{{{r}^{2}}+{{s}^{2}}}{{{r}^{2}}-{{s}^{2}}};r\ \ne \pm s,\ o)\ \frac{{{m}^{2}}+{{n}^{2}}}{{{m}^{2}}-{{n}^{2}}};\ m\ne \pm n,\$ $\displaystyle p)\ \frac{9u+5v}{{{u}^{2}}-{{v}^{2}}};\ u\ne \pm v,\ q)\ \frac{2z\left( z-6 \right)}{{{z}^{2}}-9};\ z\ne \pm 3$

15) $\displaystyle a)\ \frac{7{{a}^{2}}+5a}{{{a}^{2}}-25};\ a\ne \pm 5,\ b)\ \frac{{{x}^{2}}+1}{{{x}^{2}}-1};\ x\ne \pm 1,\ c)\ \frac{10ab}{{{a}^{2}}-{{b}^{2}}};\ a\ne \pm b,$ $\displaystyle d)\ \frac{7a+3b}{5\left( a-b \right)\left( a+b \right)};\ a\ne \pm b,\ e)\ \frac{5{{u}^{2}}-9uv}{3\left( u+v \right)\left( u-v \right)};\ u\ne \pm v,$ $\displaystyle f)\ \frac{4a-{{b}^{2}}}{ab\left( x+y \right)};\ a\ne 0,\,\,b\ne 0,\,\,x\ne -y,\ g)\ \frac{2{{r}^{2}}+rs+3{{s}^{2}}}{5\left( r+s \right)\left( r-s \right)};\ r\ne \pm s,$ $\displaystyle h)\ \frac{a}{4\left( a-1 \right)};\ a\ne 1,\ i)\ \frac{{{x}^{2}}+4x+37}{2\left( x-3 \right)\left( x+3 \right)};\,x\ne \pm 3,\ j)\ \frac{1}{2\left( y-2 \right)};\,y\ne \pm 2,$ $\displaystyle k)\ \frac{15}{\left( a+3 \right)\left( a-3 \right)};\,a\ne \pm 3,\ l)\ \frac{m\left( 1+2x \right)}{\left( 1-x \right)\left( 1+x \right)};\,x\ne \pm 1,\$ $\displaystyle m)\ \frac{3t+2}{2\left( t+1 \right)\left( t+2 \right)};t\ne -1,\,t\ne -2,\ n)\ \frac{a+1}{{{\left( a+b \right)}^{2}}};\,a\ne -b,\$ $\displaystyle o)\ \frac{5x}{{{\left( x+y \right)}^{2}}};\,x\ne -y,$

16) $\displaystyle a)\ \frac{2u}{{{\left( u-v \right)}^{2}}};\ u\ne v,\ b)\ \frac{1}{r+s};\ r\ne -s,\ c)\ \frac{xy+1}{{{\left( y-1 \right)}^{2}}};\ y\ne 1,\$ $\displaystyle d)\ \frac{2x+y+10}{x+y};\ x\ne -y,\ e)\ \frac{3{{a}^{2}}-3a+1}{a\left( a-1 \right)};\ a\ne 0,\,a\ne 1,\$ $\displaystyle f)\ \frac{m-2}{\left( m-1 \right)\left( m+1 \right)};\ m\ne \pm 1,\ g)\ \frac{-s}{12\left( r-s \right)};\ r\ne s,\$ $\displaystyle h)\ \frac{{{a}^{2}}+2}{a\left( b+c \right)};\ a\ne 0,\,b\ne -c,\ i)\ \frac{3\left( n+1 \right)}{x-1};\ x\ne 1,\ j)\ 0;\ a\ne 0,\,a\ne b,\$ $\displaystyle k)\ -1;\ a\ne \pm b,\ l)\ \frac{15n+8}{4{{n}^{2}}-9};\ n\ne \pm \frac{3}{2},\ m)\ \frac{5-6p}{9{{p}^{2}}-4};\ p\ne \pm \frac{2}{3},\$ $\displaystyle n)\ -\frac{1}{a};\ a\ne 0,\,a\ne \frac{1}{2},\ o)\ \frac{4{{b}^{2}}}{{{\left( a+b \right)}^{2}}{{\left( a-b \right)}^{2}}};\ a\ne \pm b,$

17) $\displaystyle a)\ \frac{{{x}^{2}}+2x+2}{2x\left( {{x}^{2}}-1 \right)};\ x\ne 0,\,x\ne \pm 1,\ b)\ \frac{2a}{{{\left( a-2 \right)}^{2}}\left( a+2 \right)};\ a\ne \pm 2,\ c)\ a-1;\ a\ne 0,\$ $\displaystyle d)\,\frac{5{{x}^{2}}-x-2}{x\left( {{x}^{2}}-4 \right)};x\ne 0,\,x\ne \pm 2,\,e)\,\frac{10x}{{{\left( x-3 \right)}^{2}}\left( x+3 \right)};x\ne \pm 3,\,f)\,\frac{{{x}^{2}}+1}{{{x}^{2}}-1};x\ne \pm 1$ $\displaystyle g)\ \frac{mn}{{{\left( m+n \right)}^{2}}};m\ne -n,\ h)\ \frac{2ab-{{b}^{2}}}{a\left( a-b \right)};a\ne 0,\,b\ne 0,\ i)\ \frac{1}{n\left( n-1 \right)};n\ne 0,\,n\ne 1,$

18) $\displaystyle a)\ \frac{ab}{{{a}^{2}}-{{b}^{2}}},\ a\ne \pm b;\ b)\ \frac{1}{1-{{m}^{2}}},\ m\ne \pm 1;\ c)\ -\frac{4}{{{u}^{2}}-1},\ u\ne \pm 1;\$ $\displaystyle d)\ \frac{{{a}^{4}}-{{a}^{3}}+{{a}^{2}}-a+1}{{{a}^{5}}},\ a\ne 0;\ e)\ \frac{{{x}^{2}}}{1-{{x}^{2}}},\ x\ne \pm 1;\ f)\ \frac{x-y}{x+y},\ x\ne \pm y;\$

Násobení:

1) $\displaystyle a)\ \frac{a}{3};\,p\ne 0;\ b)\ \frac{1}{6{{v}^{2}}};\,u\ne 0,\,v\ne 0;\ c)-\frac{2pq}{3};\,q\ne 0;\ d)\ \frac{5n}{3};\,m\ne 0,\,n\ne 0;\$ $\displaystyle e)\ \frac{ab}{c};\,a\ne 0,\,b\ne 0,\,c\ne 0;\ f)-\frac{1}{3y};\,x\ne 0,\,y\ne 0;\$ $\displaystyle g)\ \frac{5x}{14b};\,a\ne 0,\,b\ne 0,\,x\ne 0,\,y\ne 0;\ h)\ \frac{21{{n}^{3}}}{5m};\,m\ne 0;\ i)\ \frac{1}{5{{b}^{2}}};\,a,b,x,y,z\ne 0;$ $\displaystyle j)-\frac{12{{x}^{2}}}{5{{a}^{2}}b};\,a\ne 0,\,b\ne 0;\ k)\ \frac{8{{p}^{2}}}{15r{{s}^{3}}};\,r,s,q\ne 0;\ l) -1;\,a\ne 0,\,b\ne 0;\$

2) $\displaystyle a)\ \frac{2x}{3y};\,x,y\ne 0,\,x\ne -1;\,b)\ \frac{a}{2b};\,b\ne 0,\,a\ne b;\,c)\ c+6;\,c,d\ne 0;$ $\displaystyle d)\ \frac{2}{7\left( m+1 \right)};\,m\ne 0,\,m\ne -1;\,e)\ \frac{2}{3};\,q\ne 2,\,p\ne -q;\,f)\ \frac{3\left( a+b \right)}{2\left( x-y \right)};\,x\ne \pm y,\,a\ne b;$ $\displaystyle g)\ \frac{{{a}^{2}}}{{{b}^{2}}};\,a,b\ne 0,\,a\ne \pm b;\,h)\ \frac{{{r}^{2}}}{r-s};\,r\ne \pm s;\,i)\ 1;\,a,b\ne 0,\,a\ne -b;$ $\displaystyle j)\ \frac{2\left( x-y \right)}{{{x}^{2}}};\,x\ne 0,\,x\ne -y;\,k)\ \frac{5n\left( 1+n \right)}{n-1};\,n\ne \pm 1;\,l)\ ab;\,a\ne \pm b;\,m)\ 1;\,x\ne \pm y;$ $\displaystyle n)\ \frac{3}{4};\,c\ne \pm d;\,o)\ \frac{{{z}^{2}}}{z-3};\,z\ne 3,\,z\ne -1;$

3) $\displaystyle a)\ \frac{3}{2};\,x\ne \pm 1;\ b)\ \frac{a}{a-2};\,a\ne 2;a\ne -b;\,a,b\ne 0;\$ $\displaystyle c)\ \left( r+3 \right)\left( r-1 \right);\,r\ne -1;\,r\ne 3;\ d)\ m-n;\,m\ne -n;\,m,n\ne 0;\$ $\displaystyle e)\ \frac{2}{v};\,u\ne v;\,u,v\ne 0;\ f)\ \frac{q\left( p+q \right)}{10\left( p-1 \right)};\,p\ne \pm q;\,p\ne 0;\,p\ne 1;\$ $\displaystyle g)\ \frac{4}{5};\,a\ne \pm n;\ h)\ 2\left( 1+a \right);\,a\ne \pm 2;\,a\ne 1;$ $\displaystyle i)\ 2\left( 1+x \right);\,x\ne \pm 2;\,x\ne 1;$ $\displaystyle j)\ \frac{3\left( x+y \right)}{\left( a+b \right)\left( x-y \right)};\,a\ne \pm b;\,x\ne y;\ k)\ \frac{{{\left( x+2 \right)}^{2}}}{2};\,x\ne \pm 2;\$ $\displaystyle l)\ \frac{3}{4};\,z\ne \pm 1;\ m)\ \frac{a-2b}{{{a}^{3}}};\,a\ne b;a\,\ne 0;\,a\ne -2b\ n)\ {{r}^{2}}-1;\,r\ne \pm 1;\$

4) $\displaystyle a)\ \frac{{{r}^{2}}{{s}^{2}}}{{{r}^{2}}+2rs+{{s}^{2}}};\,r\ne -s;\ b)\ \frac{{{x}^{2}}+2xy+{{y}^{2}}}{{{x}^{2}}-2xy+{{y}^{2}}};\,x\ne y;\ c)\ \frac{{{a}^{2}}-2a+1}{{{b}^{2}}+6b+9};\,b\ne -3;$ $\displaystyle d)\ \frac{25+10m+{{m}^{2}}}{{{n}^{2}}-8n+16};\,n\ne 4;\ e)\ \frac{4{{p}^{2}}-4pq+{{q}^{2}}}{{{p}^{2}}+14pq+{{q}^{2}}};\,p\ne -7q;\ f)\ \frac{{{u}^{4}}+18{{u}^{2}}+81}{49{{z}^{6}}};\,z\ne 0;$ $\displaystyle g)\ \frac{4{{a}^{4}}-40{{a}^{2}}+100}{25{{a}^{6}}};\,a\ne 0;\ h)\ 4{{x}^{2}}+8xy+4{{y}^{2}};\,i)\ \frac{{{b}^{2}}+2ab+{{a}^{2}}}{{{a}^{2}}{{b}^{2}}};\,a,b\ne 0;$ $\displaystyle j)\ \frac{{{a}^{2}}{{y}^{2}}+2abxy+{{b}^{2}}{{x}^{2}}}{{{x}^{2}}{{y}^{2}}};\,x,y\ne 0;\ k)\ \frac{{{m}^{2}}+6m+9}{9};\ l)\ \frac{{{m}^{2}}{{n}^{2}}-20mn+100}{{{n}^{4}}};\,n\ne 0;$ $\displaystyle m)\ \frac{{{x}^{2}}}{36{{y}^{2}}};\,y\ne 0;\ n)\ \frac{{{a}^{4}}}{{{b}^{2}}{{c}^{2}}};\,b,c\ne 0;\ o)\ \frac{{{r}^{4}}+2{{r}^{2}}p+{{p}^{2}}}{{{r}^{2}}};\,r\ne 0;$

5) $\displaystyle a)\ \frac{{{a}^{2}}-{{b}^{2}}}{ab};\,a,b\ne 0;\ b)\ bc+ac+ab;\,a,b,c\ne 0;\ c)\ \frac{{{\left( r+s \right)}^{2}}}{s};\,s\ne 0;$ $\displaystyle d)\ \frac{25-{{x}^{2}}}{5x};\,x\ne 0;\ e)\ \frac{1}{b\left( a-b \right)};\,a,b\ne 0;\ f)\ x-y;\,x,y\ne 0;\,x\ne -y;$ $\displaystyle g)\ \frac{m}{3n};\,m,n\ne 0;\,m\ne n;\ h)\ x-1;\,x\ne 0;\,x\ne -1;$ $\displaystyle i)\ x-y;\,x\ne 0;\,x\ne y;\ j)\ {{z}^{2}}+1;\,z\ne \pm 1;$

6) $\displaystyle a)\ 1;\,x\ne -\frac{3}{2};\,x\ne -\frac{1}{5};\ b)\ \frac{u-v}{u+v};\,u\ne \pm v;\$ $\displaystyle c)\ 5;\,a\,\ne \pm b;\ d)\ c;\,c\ne 0;\,c\ne -1;$

Dělení:

1) $\displaystyle a)\ -\frac{3}{4};\,a,b\ne 0;\ b)\ \frac{4{{s}^{2}}}{15{{p}^{2}}};\,p,r,s\ne 0;\ c)\ \frac{4}{9xy};\,x,y\ne 0;\ d)\ 6{{a}^{3}}b;\,a,b\ne 0;$ $\displaystyle e)\ \frac{{{a}^{2}}}{{{b}^{2}}};\,a,b\ne 0;\ f)\ \frac{{{x}^{2}}+6r}{2x};\,r,x\ne 0;\ g)\ \frac{3uv}{50{{z}^{3}}};\,z\ne 0;\ h)\ 3a{{d}^{2}};\,a,b,c,d\ne 0;$ $\displaystyle i)\ \frac{a}{b};\,a,b,c\ne 0;\ j)\ -\frac{3v}{4u{{x}^{2}}z};\,u,v,x,z\ne 0;\ k)\ {{a}^{2}};\,a,b,m,n\ne 0;\ l)\ \frac{1}{2};\,r,s\ne 0;$

2) $\displaystyle a)\ \frac{a+b}{2x};\ a,x\ne 0;\ b)\ \frac{2}{d};\ d\ne 0;\ c\ne 1;\ c)\ 2\left( t-2 \right);\ t\ne 0;$ $\displaystyle d)\ \frac{3\left( s-2 \right)}{s+5};\ s\ne -5;\ s\ne 2;\ e)\ {{x}^{2}};\ y\ne 0;\ x\ne y;\ f)\ -1;\ a\ne b;$ $\displaystyle g)\ \frac{2}{3};\ a\ne -b;\ b\ne 2;\ h)\ \frac{2x}{5y};\ x,y\ne 0;\ x\ne -1;$ $\displaystyle i)\ \frac{{{y}^{2}}}{7\left( y-3 \right)};\,y\ne 3;\,y\ne -1;\,j)\ 2;\,a\ne 0;$ $\displaystyle k)\ \frac{2\left( m-n \right)}{m};\,m\ne 0;\,m\ne -3;\,m\ne n;\ l)\ 5r;r\,\ne 0;\,r\ne \pm 1;\ m)\ 1;\,x\ne \pm y;$ $\displaystyle n)\ \frac{v-1}{v\left( v+1 \right)};\,v\ne 0;\,v\ne -1;\ o)\ \frac{2\left( r+3 \right)}{r};\,r\ne 0;\,r\ne \pm 3;\ p)\ \frac{2}{3};\,y\ne 2;\,x\ne -y;$ $\displaystyle q)\ {{\left( a+b \right)}^{2}};\,a,b\ne 0;\,a\ne -b;\ r)\ \frac{a}{9};\,a\ne 0;\,a\ne \pm b;$

3) $\displaystyle a)\ \frac{3}{2{{\left( 1+x \right)}^{2}}};\,x\ne \pm 1;\ b)\ \frac{4}{5};\,u\ne \pm v;\ c)\ \frac{a+b}{a+3};\,a\ne \pm b;\,a\ne -3;$ $\displaystyle d)\ 1;\,p\ne \pm q;\ e)\ \frac{{{\left( a+2 \right)}^{2}}}{2};\,a\ne \pm 2;$ $\displaystyle f)\ \frac{3}{x-y};\,x\ne \pm y;\ g)\ \frac{1}{3};\,v\ne 3;\,v\ne 0;\,v\ne -1;$ $\displaystyle h)\ \frac{a}{7};\,a\ne \pm 5;\,a\ne 0;\ i)\ \frac{{{x}^{2}}-4}{4{{x}^{3}}};\,x\ne 2;\,x\ne 0;$ $\displaystyle j)\ \frac{x-2y}{{{x}^{2}}};x\ne -2y;\,x\ne 0;\,x\ne y;$ $\displaystyle k)\ u-v;\,u\ne -v;\,u,v\ne 0;\ l)\ \frac{1}{{{a}^{2}}b};\,a\ne b;\,a,b\ne 0;$

4) $\displaystyle a)\ x-2;\,x\ne 0;\,x\ne -2;\ b)\ 2y;\,y\ne -2;\ c)\ \frac{m}{n};\,m\ne 0;\,m\ne n;$ $\displaystyle d)\ 3r;\,r\ne 0;\,r\ne -s;\ e)\ \frac{{{x}^{2}}}{3x+1};\,x\ne 0;\,x\ne -\frac{1}{3};\ f)\ \frac{{{p}^{2}}-1}{p};\,p\ne 0;$

5) $\displaystyle a)\ 1;\,x\ne -\frac{3}{2};\ b)\ 2\left( {{a}^{2}}+{{b}^{2}} \right);\,a,b\ne 0;\,a\ne -b;$ $\displaystyle c)\ \frac{x+a}{x-a};\,a\ne 0;\,x\ne \pm a;\ d)\ \frac{1}{a};\,a\ne 0;\,a\ne 1;$ $\displaystyle e)\ \frac{20}{3};\,a\ne \pm 1;\ f)\ \frac{1}{a+b};\,a,b\ne 0;\,a\ne -b;$ $\displaystyle g)\ -m;\,m\ne 0;\,m\ne 1;\ h)\ d\left( c-d \right);\,c\ne 0;\,c\ne d;$

Složené lomené výrazy:

1) $\displaystyle a)\ m+n;\,m,n\ne 0;\,b)\ \frac{3}{10{{v}^{4}}};\,u,v\ne 0;\,c)\ \frac{a}{y};\,x,y\ne 0;\,x\ne -y;$ $\displaystyle d)\ \frac{1}{{a}^{2}-{b}^{2}};\,a\ne \pm b;\,e)\ \frac{x}{x-y};\,x\,\ne \pm y;\,f)\ \frac{r}{9};\,r\ne \pm s;$

2) $\displaystyle a)\ \frac{1}{a\left( a-2 \right)};\,a\ne 0;\,a\ne \pm 2;\ b)\ \frac{z-2}{z};\,z\ne 0;\,z\ne -2;\ c)\ 1;\,p,q\ne 0;\,p\ne -q;$ $\displaystyle d)\ \frac{5}{2\left( h-1 \right)};\,k\ne 0;\,h\ne \pm 1;\ e)\ \frac{3}{4};\,u\ne \pm v;\ f)\ \frac{1}{n-m};\,n\ne 0;\,m\ne \pm n;$

3) $\displaystyle a)\ 1;\,a\ne \pm b;\ b)\ \frac{y+x}{y-x};\,x,y\ne 0;\,x\ne y;$ $\displaystyle c)\ 2;\,m,n\ne 0;\,m\ne -n;\ d)\ \frac{a+b}{a-b};\,a\ne 0;\,a\ne b;$ $\displaystyle e)\ \frac{x}{x-y};\,x\ne 0;\,x\ne \pm y;\ f)\ a-b;\,a,b\ne 0;\,a\ne b;$

4) $b) \, \frac{2a}{1+a^{2}};$ $e)\, \frac{v\left ( u-v \right )}{u\left ( u+v \right )};$