Sčítání a odčítání

1) Vypočtěte:

$\displaystyle a)\quad \frac{5u}{8}+\frac{u}{8}+\frac{3u}{8}=$

$\displaystyle b)\quad \frac{c+5}{y}-\frac{3}{y}=$

$\displaystyle c)\quad \frac{14ab}{15}+\frac{ab}{15}-\frac{3ab}{15}=$

$\displaystyle d)\quad \frac{r+3}{p}-\frac{r+1}{p}=$

$\displaystyle e)\quad \frac{2x+y}{y}-\frac{3x+y}{y}+\frac{x+2y}{y}=$

$\displaystyle f)\quad \frac{5+3c}{2d}-\frac{1-c}{2d}-\frac{2+4c}{2d}=$

2) Vypočtěte:

$\displaystyle a)\quad 2+\frac{m}{5}=$

$\displaystyle b)\quad r-\frac{r}{3}=$

$\displaystyle c)\quad \frac{1}{2}+a=$

$\displaystyle d)\quad \frac{a}{b}-1=$

$\displaystyle e)\quad \frac{x}{5}-x=$

$\displaystyle f)\quad y-\frac{y}{4}=$

$\displaystyle g)\quad 3-\frac{u}{v}=$

$\displaystyle h)\quad a+\frac{a}{b}=$

$\displaystyle i)\quad \frac{1}{s}-s=$

3) Vypočtěte:

$\displaystyle a)\quad \frac{a}{2}+\frac{a}{4}=$

$\displaystyle b)\quad \frac{x}{3}+\frac{y}{4}+\frac{z}{6}=$

$\displaystyle c)\quad \frac{2r}{3}+\frac{r}{2}-\frac{5r}{9}=$

$\displaystyle d)\quad \frac{7x}{3}+\frac{4x}{6}=$

$\displaystyle e)\quad \frac{2a}{15}-\frac{3a}{20}+\frac{a}{12}=$

$\displaystyle f)\quad \frac{{{a}^{2}}}{6}+\frac{3a}{2}-\frac{2{{a}^{2}}}{15}-\frac{5a}{3}=$

$\displaystyle g)\quad \frac{{{z}^{2}}}{2}-\frac{2{{z}^{2}}}{5}=$

$\displaystyle h)\quad x-\frac{3y}{4}-\frac{5x}{2}+\frac{4y}{5}=$

$\displaystyle i)\quad \frac{4s}{7}+1-\frac{s}{3}+s=$

4) Vypočtěte:

$\displaystyle a)\quad \frac{2}{a}+\frac{5}{b}=$

$\displaystyle b)\quad \frac{n}{2a}-\frac{n}{3a}=$

$\displaystyle c)\quad \frac{7x}{3b}+\frac{4x}{6b}=$

$\displaystyle d)\quad \frac{s}{6x}+\frac{3s}{4x}=$

$\displaystyle e)\quad \frac{{{z}^{2}}}{2z}-\frac{2{{z}^{2}}}{5z}=$

$\displaystyle f)\quad \frac{a}{6t}+\frac{b}{8t}=$

5) Vypočtěte:

$\displaystyle a)\quad \frac{3}{4}+\frac{x}{y}=$

$\displaystyle b)\quad \frac{4}{5m}-\frac{1}{2m}=$

$\displaystyle c)\quad \frac{1}{5}-\frac{2}{h}=$

$\displaystyle d)\quad \frac{a}{2x}+\frac{b}{4x}=$

$\displaystyle e)\quad \frac{2x}{3y}-\frac{y}{x}=$

$\displaystyle f)\quad \frac{7c}{10d}+\frac{5c}{4d}=$

6) Vypočtěte:

$\displaystyle a)\quad \frac{3m}{10}-\frac{n}{6}+\frac{m}{5}=$

$\displaystyle b)\quad \frac{a}{bc}+\frac{b}{ac}+\frac{c}{ab}=$

$\displaystyle c)\quad \frac{1}{{{r}^{2}}}+\frac{2s}{{{r}^{3}}}+\frac{{{s}^{2}}}{{{r}^{4}}}=$

$\displaystyle d)\quad \frac{2}{x}+\frac{5}{2x}-\frac{2}{4x}=$

$\displaystyle e)\quad \frac{r}{2s}+\frac{2r}{3s}-\frac{3r}{4s}=$

$\displaystyle f)\quad \frac{1}{x}+\frac{1}{y}+\frac{1}{z}=$

7) Vypočtěte:

$\displaystyle a)\quad \frac{1}{6ab}+\frac{2}{5ab}=$

$\displaystyle b)\quad \frac{u}{6s}-\frac{v}{8t}=$

$\displaystyle c)\quad \frac{4a}{5b}-\frac{3a}{4b}=$

$\displaystyle d)\quad \frac{5p}{6q}-\frac{7p}{30q}=$

$\displaystyle e)\quad \frac{x}{12y}+\frac{y}{18y}=$

$\displaystyle f)\quad \frac{c}{ab}-\frac{b}{ac}=$

8) Vypočtěte:

$\displaystyle a)\quad \frac{y}{2}+\frac{x}{y}+2=$

$\displaystyle b)\quad 1+\frac{a}{b}+a=$

$\displaystyle c)\quad \frac{3x+1}{4}-\frac{x}{2}=$

$\displaystyle d)\quad \frac{v+3}{4}+\frac{v-6}{8}=$

$\displaystyle e)\quad \frac{2z-3}{3}+\frac{z+1}{2}=$

$\displaystyle f)\quad \frac{2a-3}{4}+\frac{5a+3}{3}=$

$\displaystyle g)\quad \frac{4x+3y}{10}-\frac{2x-y}{15}=$

$\displaystyle h)\quad \frac{4p-5q}{12}-\frac{3p-2q}{18}=$

$\displaystyle i)\quad \frac{{{x}^{2}}}{{{y}^{2}}}-\frac{2x}{y}+1=$

$\displaystyle j)\quad 3-\frac{1}{a}+\frac{a+1}{a}=$

$\displaystyle k)\quad \frac{n+1}{3}-\frac{n+2}{5}=$

$\displaystyle l)\quad \frac{2a-3b}{12}-\frac{a-3b}{8}=$

$\displaystyle m)\quad \frac{7r+2s}{4}+\frac{3r-s}{6}=$

$\displaystyle n)\quad \frac{4ab-ac}{7}+\frac{3ac-11ab}{21}=$

$\displaystyle o)\quad \frac{3{{s}^{2}}-2{{r}^{2}}}{5}-\frac{5{{r}^{2}}-{{s}^{2}}}{4}=$

$\displaystyle p)\quad \frac{m-3n}{12}-\frac{2m-n}{8}=$

9) Vypočtěte:

$\displaystyle a)\quad \frac{x}{ab}+\frac{x}{ac}=$

$\displaystyle b)\quad \frac{r+10}{2p}+\frac{2r-5}{p}=$

$\displaystyle c)\quad \frac{2a-3b}{a}+\frac{{{a}^{2}}+4{{b}^{2}}}{ab}=$

$\displaystyle d)\quad \frac{x+3y}{y}-\frac{2x-y}{x}=$

$\displaystyle e)\quad \frac{a+1}{ax}-\frac{b-1}{bx}=$

$\displaystyle f)\quad \frac{5u-2v}{7v}-\frac{u+4}{2v}=$

10) Vypočtěte:

$\displaystyle a)\quad \frac{2a+3b}{2}-\frac{a-2b}{3}+\frac{a-b}{4}=$

$\displaystyle b)\quad \frac{n-1}{2}+\frac{3n-1}{4}-\frac{5n-1}{6}=$

$\displaystyle c)\quad \frac{2\left( r-s \right)}{3}-\frac{3\left( r-1 \right)}{5}+\frac{s+1}{2}=$

$\displaystyle d)\quad \frac{5\left( 2x-y \right)}{8}-\frac{3\left( x-4y \right)}{2}+\frac{7\left( x-y \right)}{6}=$

11) Vypočtěte:

$\displaystyle a)\quad \frac{2a}{{{x}^{3}}}-\frac{3}{x}=$

$\displaystyle b)\quad \frac{c}{{{d}^{2}}}+\frac{d}{{{c}^{3}}}=$

$\displaystyle c)\quad \frac{1}{{{x}^{4}}{{y}^{3}}}+\frac{2}{{{x}^{3}}{{y}^{4}}}=$

$\displaystyle d)\quad \frac{3}{{{a}^{2}}{{b}^{3}}}-\frac{4}{{{a}^{4}}{{b}^{2}}}=$

$\displaystyle e)\quad \frac{a}{2x}-\frac{b}{3{{x}^{2}}}=$

$\displaystyle f)\quad \frac{3x}{4{{a}^{2}}b}+\frac{5x}{2a{{b}^{2}}}-\frac{1}{6{{a}^{2}}b}=$

$\displaystyle g)\quad \frac{5t}{uv}+\frac{2z}{3{{u}^{2}}v}-\frac{7}{6{{u}^{2}}{{v}^{2}}}=$

$\displaystyle h)\quad \frac{2a-3b}{{{a}^{2}}b}-\frac{4a-5b}{a{{b}^{2}}}=$

$\displaystyle i)\quad \frac{5{{r}^{2}}-3s}{{{r}^{2}}s}+\frac{6r-2{{s}^{2}}}{{{r}^{2}}{{s}^{2}}}=$

$\displaystyle j)\quad \frac{2{{a}^{2}}+3a-5}{{{a}^{2}}b}+\frac{4a-1}{ab}=$

$\displaystyle k)\quad \frac{5{{x}^{2}}-2x-1}{{{x}^{2}}y}-\frac{3x-2}{xy}=$

12) Vypočtěte:

$\displaystyle a)\quad \frac{2{{x}^{2}}y-y}{x}-xy=$

$\displaystyle b)\quad \frac{a+b}{3}-a+b=$

$\displaystyle c)\quad \frac{x+1}{a-b}+\frac{x-1}{a-b}=$

$\displaystyle d)\quad \frac{a}{x+y}-\frac{a-3}{x+y}=$

$\displaystyle e)\quad \frac{m-4}{n+2}+\frac{m-3}{2+n}=$

$\displaystyle f)\quad \frac{2x}{a-b}+\frac{x}{b-a}=$

$\displaystyle g)\quad \frac{u}{y-1}-\frac{v}{1-y}=$

$\displaystyle h)\quad m-\frac{m-1}{2}+\frac{m-2}{3}=$

$\displaystyle i)\quad u-v-\frac{u-v}{4}=$

$\displaystyle j)\quad \frac{3a+1}{5v+z}-\frac{2a+3}{z+5v}=$

$\displaystyle k)\quad \frac{2r}{r+s}-\frac{r-5}{s+r}=$

$\displaystyle l)\quad \frac{5z-7}{uv-{{v}^{2}}}+\frac{3z-8}{uv-{{v}^{2}}}=$

$\displaystyle m)\quad \frac{9}{r-3}+\frac{8}{3-r}=$

$\displaystyle n)\quad \frac{5{{a}^{2}}}{b-2}-\frac{2{{a}^{2}}}{2-b}=$

$\displaystyle o)\quad \frac{a+1}{a-1}+\frac{a-2}{1-a}=$

$\displaystyle p)\quad \frac{m}{2p-q}+\frac{n}{q-2p}=$

$\displaystyle q)\quad \frac{3r+9}{5{{r}^{2}}+s}-\frac{2r-11}{s+5{{r}^{2}}}=$

$\displaystyle r)\quad \frac{a}{{{x}^{2}}-1}-\frac{b}{1-{{x}^{2}}}=$

$\displaystyle s)\quad \frac{a-5}{a-3}+\frac{a+5}{3-a}=$

$\displaystyle t)\quad \frac{1}{u-v}+\frac{2}{v-u}=$

$\displaystyle u)\quad \frac{c+1}{a-b}-\frac{c+2}{b-a}-\frac{c-1}{a-b}=$

$\displaystyle v)\quad \frac{a}{x-y}-\frac{b}{y-x}+\frac{c}{\begin{array}{l}x-y\\\end{array}}=$

13) Vypočtěte:

$\displaystyle a)\quad 1+\frac{1}{a-1}=$

$\displaystyle b)\quad 1-\frac{2x}{x+1}=$

$\displaystyle c)\quad \frac{1}{1+y}-1=$

$\displaystyle d)\quad t-\frac{st}{s-t}=$

$\displaystyle e)\quad 1-\frac{2p}{p+1}=$

$\displaystyle f)\quad \frac{2}{z+1}-2=$

$\displaystyle g)\quad 3-\frac{6a}{2a+4}=$

$\displaystyle h)\quad \frac{2s}{r+s}-2=$

$\displaystyle i)\quad 1+\frac{7d}{c-2d}=$

$\displaystyle j)\quad \frac{8s}{r+s}-8=$

$\displaystyle k)\quad \frac{a-4b}{2b+5}+2=$

$\displaystyle l)\quad \frac{5}{3\left( x+y \right)}+\frac{2}{x+y}=$

$\displaystyle m)\quad \frac{3m}{m-1}-\frac{3m}{2\left( m-1 \right)}=$

$\displaystyle n)\quad \frac{9a}{4\left( a+2 \right)}-\frac{1}{a+2}=$

$\displaystyle o)\quad \frac{x}{1-y}+\frac{{{y}^{2}}}{x\left( 1-y \right)}=$

$\displaystyle p)\quad \frac{5a}{2\left( a+b \right)}-\frac{7a}{3\left( b+a \right)}=$

$\displaystyle q)\quad \frac{4r+1}{5\left( p-3 \right)}-\frac{r}{2\left( p-3 \right)}=$

14) Vypočtěte:

$\displaystyle a)\quad \frac{3}{2x+2}+\frac{9}{4x+4}=$

$\displaystyle b)\quad \frac{7}{5a-5}-\frac{11}{10a-10}=$

$\displaystyle c)\quad \frac{a}{3\left( a+b \right)}-\frac{2a}{6a+6b}=$

$\displaystyle d)\quad \frac{1}{x+y}+\frac{1}{x-y}=$

$\displaystyle e)\quad \frac{1}{a-b}-\frac{1}{a+b}=$

$\displaystyle f)\quad \frac{1}{2r-s}+\frac{1}{2r+s}=$

$\displaystyle g)\quad \frac{3}{y-1}+\frac{1-3y}{{{y}^{2}}-y}=$

$\displaystyle h)\quad \frac{3x}{4x+4y}-\frac{x}{8x+8y}=$

$\displaystyle i)\quad \frac{a+c}{ac-bc}+\frac{a-1}{2\left( a-b \right)}=$

$\displaystyle j)\quad \frac{3}{m+n}+\frac{2}{m-n}=$

$\displaystyle k)\quad \frac{5}{v-2}-\frac{5}{v+2}=$

$\displaystyle l)\quad \frac{4}{p-q}-\frac{2}{p+q}=$

$\displaystyle m)\quad \frac{p}{q-2}-\frac{p}{q+2}=$

$\displaystyle n)\quad \frac{r}{r+s}+\frac{s}{r-s}=$

$\displaystyle o)\quad \frac{m}{m-n}-\frac{n}{m+n}=$

$\displaystyle p)\quad \frac{7}{u-v}+\frac{2}{u+v}=$

$\displaystyle q)\quad \frac{3z}{3+z}-\frac{z}{z-3}=$

15) Vypočtěte:

$\displaystyle a)\quad \frac{3a}{a+5}+\frac{4a}{a-5}=$

$\displaystyle b)\quad \frac{x}{x-1}-\frac{1}{1+x}=$

$\displaystyle c)\quad \frac{2a+3b}{a-b}-\frac{2a-3b}{a+b}=$

$\displaystyle d)\quad \frac{2}{5a+5b}+\frac{1}{a-b}=$

$\displaystyle e)\quad \frac{7u}{3u+3v}-\frac{2u}{3u-3v}=$

$\displaystyle f)\quad \frac{a-b}{ax+ay}+\frac{4-b}{bx+by}=$

$\displaystyle g)\quad \frac{2r}{5r+5s}+\frac{3s}{5\left( r-s \right)}=$

$\displaystyle h)\quad \frac{3a}{2a-2}-\frac{5a}{4a-4}=$

$\displaystyle i)\quad \frac{5}{x-3}-\frac{x-2}{{{x}^{2}}-9}+\frac{x-1}{2x+6}=$

$\displaystyle j)\quad \frac{7}{2y-4}-\frac{3}{y+2}-\frac{12}{{{y}^{2}}-4}=$

$\displaystyle k)\quad \frac{a\left( a-8 \right)}{{{a}^{2}}-9}+\frac{5}{a-3}-\frac{a}{a+3}=$

$\displaystyle l)\quad \frac{m}{1-x}-\frac{m}{1+x}+\frac{m}{1-{{x}^{2}}}=$

$\displaystyle m)\quad \frac{1}{t+1}+\frac{2}{t+2}-\frac{3}{2t+2}=$

$\displaystyle n)\quad \frac{2a+1}{{{a}^{2}}+2ab+{{b}^{2}}}-\frac{a}{{{\left( a+b \right)}^{2}}}=$

$\displaystyle o)\quad \frac{3x-2y}{{{x}^{2}}+2xy+{{y}^{2}}}+\frac{2}{x+y}=$

16) Vypočtěte:

$\displaystyle a)\quad \frac{2}{u-v}+\frac{2v}{{{\left( u-v \right)}^{2}}}=$

$\displaystyle b)\quad \frac{5r+5s}{{{r}^{2}}+2rs+{{s}^{2}}}-\frac{4}{r+s}=$

$\displaystyle c)\quad \frac{x-1}{y-1}+\frac{x+y}{{{y}^{2}}-2y+1}=$

$\displaystyle d)\quad \frac{2x-3y+1}{x+y}+\frac{9+4y}{y+x}=$

$\displaystyle e)\quad \frac{3a}{a-1}+\frac{1-3a}{{{a}^{2}}-a}=$

$\displaystyle f)\quad \frac{2}{m+1}-\frac{m}{{{m}^{2}}-1}=$

$\displaystyle g)\quad \frac{2s}{3r-3s}-\frac{3s}{4\left( r-s \right)}=$

$\displaystyle h)\quad \frac{2}{ab+ac}+\frac{a}{b+c}=$

$\displaystyle i)\quad \frac{3n}{x-1}-\frac{3}{1-x}=$

$\displaystyle j)\quad \frac{a+b}{a}-\frac{a}{a-b}+\frac{{{b}^{2}}}{{{a}^{2}}-ab}=$

$\displaystyle k)\quad \frac{b}{a-b}-\frac{a}{a+b}-\frac{2ab}{{{a}^{2}}-{{b}^{2}}}=$

$\displaystyle l)\quad \frac{5}{2n-3}+\frac{2}{2n+3}-\frac{n-1}{9-4{{n}^{2}}}=$

$\displaystyle m)\quad \frac{1}{3p-2}-\frac{4}{2+3p}-\frac{3p-5}{4-9{{p}^{2}}}=$

$\displaystyle n)\quad \frac{2a-1}{2a}-\frac{2a}{2a-1}-\frac{1}{2a-4{{a}^{2}}}=$

$\displaystyle o)\quad \frac{1}{{{a}^{2}}+2ab+{{b}^{2}}}-\frac{2}{{{a}^{2}}-{{b}^{2}}}+\frac{1}{{{a}^{2}}-2ab+{{b}^{2}}}=$

17) Vypočtěte:

$\displaystyle a)\quad \frac{x+1}{{{x}^{2}}-x}-\frac{x+2}{2\left( {{x}^{2}}-1 \right)}=$

$\displaystyle b)\quad \frac{3+a}{{{a}^{2}}-4}+\frac{3-a}{{{\left( a-2 \right)}^{2}}}=$

$\displaystyle c)\quad \left( a-\frac{1}{a} \right)-\left( 1-\frac{1}{a} \right)=$

$\displaystyle d)\quad \frac{2x+1}{{{x}^{2}}+2x}+\frac{3x+2}{{{x}^{2}}-4}=$

$\displaystyle e)\quad \frac{2-x}{{{x}^{2}}-9}+\frac{2+x}{{{\left( x-3 \right)}^{2}}}=$

$\displaystyle f)\quad \left( \frac{1}{x-1} \right)+\left( 1- \frac{1}{x+1} \right)=$

$\displaystyle g)\quad \frac{{{m}^{2}}-2{{n}^{2}}}{{{\left( m+n \right)}^{2}}}-\frac{m-2n}{m+n}=$

$\displaystyle h)\quad \frac{a}{a-b}+\frac{a+b}{a}-2=$

$\displaystyle i)\quad 1+\frac{1}{n-1}-\frac{n+1}{n}=$

18) Vypočtěte:

$\displaystyle a)\quad \frac{2a}{a+b}+\frac{3b}{a-b}-\frac{2{{a}^{2}}+3{{b}^{2}}}{{{a}^{2}}-{{b}^{2}}}=$

$\displaystyle b)\quad \frac{1}{1+m}+\frac{1}{1-m}-\frac{1}{1-{{m}^{2}}}=$

$\displaystyle c)\quad \frac{2u-2}{{{u}^{2}}-1}-\frac{u+1}{u-1}+\frac{u-1}{u+1}=$

$\displaystyle d)\quad \frac{1}{a}-\frac{1-a}{{{a}^{2}}}+\frac{1-{{a}^{2}}}{{{a}^{3}}}-\frac{1-{{a}^{3}}}{{{a}^{4}}}+\frac{1-{{a}^{4}}}{{{a}^{5}}}=$

$\displaystyle e)\quad \frac{1+x}{1-x}-\frac{1-x}{1+x}-\frac{x\left( 4-x \right)}{1-{{x}^{2}}}=$

$\displaystyle f)\quad \frac{x-2y}{x+y}-\frac{2x-y}{y-x}-\frac{2{{x}^{2}}}{{{x}^{2}}-{{y}^{2}}}=$

$\displaystyle g)\quad \frac{3}{1-{{z}^{2}}}-\frac{2}{1-z}-\frac{1}{1+z}-\frac{z}{{{\left( 1-z \right)}^{2}}}=$

$\displaystyle h)\quad \frac{1}{{{a}^{2}}+2ab+{{b}^{2}}}-\frac{1}{{{a}^{2}}-{{b}^{2}}}+\frac{1}{a+b}-\frac{1}{a-b}=$

$\displaystyle i)\quad \frac{r}{6r+6s}-\frac{s}{3r-3s}+\frac{rs}{2{{r}^{2}}-2{{s}^{2}}}=$

$\displaystyle j)\quad \frac{1}{{{\left( a-2 \right)}^{2}}}-\frac{1}{{{a}^{2}}+4a+4}+\frac{1}{{{a}^{2}}-4}=$

$\displaystyle k)\quad \frac{2}{2+3x}-\frac{3}{3x-2}-\frac{3x}{4-9{{x}^{2}}}=$

$\displaystyle l)\quad \frac{3x+2}{{{x}^{2}}-2x+1}-\frac{6}{{{x}^{2}}-1}-\frac{3x-2}{{{x}^{2}}+2x+1}=$

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