1)      Vynásob a urči, kdy má výsledek smysl:

\displaystyle a)\quad 5p\cdot \frac{a}{15p}=

 

\displaystyle b)\quad \left( -\frac{4{{u}^{2}}}{21{{v}^{3}}} \right)\cdot \left( -\frac{7v}{8{{u}^{2}}} \right)=

 

\displaystyle c)\quad \frac{p}{6{{q}^{2}}}\cdot \left( -4{{q}^{3}} \right)=

 

\displaystyle d)\quad \frac{m}{3}\cdot \frac{{{n}^{2}}}{2m}\cdot \frac{10}{n}=

\displaystyle e)\quad \frac{{{a}^{3}}}{b}\cdot \frac{{{c}^{4}}}{{{a}^{2}}}\cdot \frac{{{b}^{2}}}{{{c}^{5}}}=

 

\displaystyle f)\quad \frac{x}{{{y}^{2}}}\cdot \frac{y}{3{{x}^{2}}}\cdot \left( -x \right)=

 

\displaystyle g)\quad \frac{3ab}{4xy}\cdot \frac{10{{x}^{2}}y}{21a{{b}^{2}}}=

 

\displaystyle h)\quad 14{{m}^{2}}{{n}^{2}}\cdot \frac{3n}{10{{m}^{3}}}=

\displaystyle i)\quad \frac{3x}{5ab}\cdot \frac{3ay}{4bz}\cdot \frac{4z}{9xy}=

 

\displaystyle j)\quad 16{{a}^{2}}{{b}^{3}}\cdot \left( -\frac{3a{{x}^{2}}}{20{{a}^{5}}{{b}^{4}}} \right)=

 

\displaystyle k)\quad \left( -\frac{2p}{qs} \right)\cdot \left( -\frac{2q}{3rs} \right)\cdot \frac{2p}{5s}=

 

\displaystyle l)\quad \left( -\frac{3{{a}^{2}}}{7b} \right)\cdot \left( -\frac{a{{b}^{2}}}{4} \right)\cdot \left( -\frac{28}{3{{a}^{3}}b} \right)=


 

2)      Vynásob a urči, kdy má výsledek smysl:

\displaystyle a)\quad \frac{{{x}^{2}}y}{3\left( x+1 \right)}\cdot \frac{2\left( x+1 \right)}{x{{y}^{2}}}=

 

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

 

\displaystyle c)\quad \frac{{{c}^{2}}+6c}{d}\cdot \frac{d}{c}=

 

\displaystyle d)\quad \frac{2m}{5m+5}\cdot \frac{5}{7m}=

 

\displaystyle e)\quad \frac{q-2}{p+q}\cdot \frac{2p+2q}{3q-6}=

\displaystyle f)\quad \frac{2{{a}^{2}}-2{{b}^{2}}}{3{{x}^{2}}-3{{y}^{2}}}\cdot \frac{9\left( x+y \right)}{4a-4b}=

 

\displaystyle g)\quad \frac{{{a}^{2}}-ab}{ab+{{b}^{2}}}\cdot \frac{{{a}^{2}}+ab}{ab-{{b}^{2}}}=

 

\displaystyle h)\quad \frac{r}{r+s}\cdot \frac{{{r}^{2}}+rs}{r-s}=

 

\displaystyle i)\quad \frac{{{a}^{2}}+ab}{a}\cdot \frac{b}{ab+{{b}^{2}}}=

 

\displaystyle j)\quad \frac{2x+8}{{{x}^{3}}}\cdot \frac{{{x}^{2}}-xy}{x+4}=

\displaystyle k)\quad \frac{15+15n}{{{n}^{2}}-1}\cdot \frac{{{n}^{3}}-n}{3n-3}=

 

\displaystyle l)\quad \frac{{{a}^{2}}-{{b}^{2}}}{a+b}\cdot \frac{ab}{a-b}=

 

\displaystyle m)\quad \frac{x+y}{x-y}\cdot \frac{{{\left( x-y \right)}^{2}}}{{{x}^{2}}-{{y}^{2}}}=

 

\displaystyle n)\quad \frac{5c-5d}{4c+4d}\cdot \frac{12c+12d}{20c-20d}=

 

\displaystyle o)\quad \frac{{{z}^{2}}+z}{4z-12}\cdot \frac{4z}{z+1}=

 


 

3)      Vynásob a urči, kdy má výsledek smysl:

\displaystyle a)\quad \frac{5-5x}{1+x}\cdot \frac{3+3x}{10-10x}=

 

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

 

\displaystyle c)\quad \frac{{{r}^{2}}-9}{r+1}\cdot \frac{{{r}^{2}}-1}{r-3}=

 

\displaystyle d)\quad \frac{{{m}^{2}}-mn}{{{m}^{2}}+mn}\cdot \frac{{{m}^{2}}n+m{{n}^{2}}}{mn}=

 

\displaystyle e)\quad \frac{4u-4v}{2uv}\cdot \frac{{{u}^{2}}}{{{u}^{2}}-uv}=

 

\displaystyle f)\quad \frac{{{p}^{2}}+pq}{5{{p}^{2}}-5{{q}^{2}}}\cdot \frac{{{p}^{2}}q-{{q}^{3}}}{2{{p}^{2}}-2p}=

 

\displaystyle g)\quad \frac{{{a}^{2}}-{{n}^{2}}}{{{\left( a+n \right)}^{2}}}\cdot \frac{4a+4n}{5\left( a-n \right)}=

 

\displaystyle h)\quad \frac{{{a}^{2}}-4}{1-a}\cdot \frac{2b}{a-2}\cdot \frac{1-{{a}^{2}}}{ab+2b}=

 

\displaystyle i)\quad \frac{{{a}^{2}}-4}{1-a}\cdot \frac{2b}{a-2}\cdot \frac{1-{{a}^{2}}}{ab+2b}=

 

\displaystyle j)\quad \frac{a{{x}^{2}}-a{{y}^{2}}}{{{\left( a+b \right)}^{2}}}\cdot \frac{3a+3b}{a{{x}^{2}}-2axy+a{{y}^{2}}}=

 

\displaystyle k)\quad \frac{2{{x}^{2}}+8x+8}{x-2}\cdot \frac{{{x}^{2}}-4}{4\left( x+2 \right)}=

 

\displaystyle l)\quad \frac{{{z}^{2}}-1}{{{z}^{2}}+2z+1}\cdot \frac{3z+3}{4z-4}=

 

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

 

\displaystyle n)\quad \frac{{{\left( r+1 \right)}^{2}}}{r-1}\cdot \frac{{{\left( r-1 \right)}^{2}}}{r+1}=


 

4)      Umocni výrazy:

\displaystyle a)\quad {{\left( \frac{rs}{r+s} \right)}^{2}}=

 

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

 

\displaystyle c)\quad {{\left( \frac{a-1}{b+3} \right)}^{2}}=

 

\displaystyle d)\quad {{\left( \frac{5+m}{n-4} \right)}^{2}}=

 

\displaystyle e)\quad {{\left( \frac{2p-q}{p+7q} \right)}^{2}}=

\displaystyle f)\quad {{\left( \frac{{{u}^{2}}+9}{7{{z}^{3}}} \right)}^{2}}=

 

\displaystyle g)\quad {{\left( \frac{2{{a}^{2}}-10}{5{{a}^{3}}} \right)}^{2}}=

 

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

 

\displaystyle i)\quad {{\left( \frac{1}{a}+\frac{1}{b} \right)}^{2}}=

 

\displaystyle j)\quad {{\left( \frac{a}{x}-\frac{b}{y} \right)}^{2}}=

\displaystyle k)\quad {{\left( \frac{m}{3}+1 \right)}^{2}}=

 

\displaystyle l)\quad {{\left( \frac{m}{n}-\frac{10}{{{n}^{2}}} \right)}^{2}}=

 

\displaystyle m)\quad {{\left( \frac{2x}{3y}-\frac{x}{2y} \right)}^{2}}=

 

\displaystyle n)\quad {{\left( \frac{a}{b} \right)}^{2}}\cdot {{\left( \frac{a}{c} \right)}^{2}}=

 

\displaystyle o)\quad {{\left( r+\frac{p}{r} \right)}^{2}}=

 


 

5)      Vynásob a urči, kdy má výsledek smysl:

\displaystyle a)\quad \left( \frac{1}{b}-\frac{1}{a} \right)\cdot \left( a+b \right)=

 

\displaystyle b)\quad abc\cdot \left( \frac{1}{a}+\frac{1}{b}+\frac{1}{c} \right)=

 

\displaystyle c)\quad \left( r+s \right)\cdot \left( 1+\frac{r}{s} \right)=

 

\displaystyle d)\quad \left( \frac{1}{x}-\frac{1}{5} \right)\cdot \left( x+5 \right)=

 

\displaystyle e)\quad \left( \frac{a}{b}+1 \right)\cdot \frac{1}{{{a}^{2}}-{{b}^{2}}}=

\displaystyle f)\quad \left( \frac{x}{y}-\frac{y}{x} \right)\cdot \frac{xy}{x+y}=

 

\displaystyle g)\quad \frac{{{m}^{2}}}{3m-3n}\cdot \left( \frac{1}{n}-\frac{1}{m} \right)=

 

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

 

\displaystyle i)\quad \left( \frac{1}{x}-\frac{2y}{{{x}^{2}}}+\frac{{{y}^{2}}}{{{x}^{3}}} \right)\cdot \frac{{{x}^{3}}}{x-y}=

 

\displaystyle j)\quad \left( {{z}^{2}}-1 \right)\cdot \left( \frac{1}{z-1}-\frac{1}{z+1}+1 \right)=


 

6)      Vynásob a urči, kdy má výsledek smysl:

\displaystyle a)\quad \frac{2x+3}{5x-1}\cdot \left( \frac{3x-2}{3+2x}+\frac{2x+1}{2x+3} \right)=

 

\displaystyle b)\quad \left( \frac{u}{u+v}+\frac{v}{u-v} \right)\cdot \left( 1-\frac{2uv}{{{u}^{2}}+{{v}^{2}}} \right)=

 

\displaystyle c)\quad \left( \frac{5a}{a+b}+\frac{5b}{a-b}+\frac{10ab}{{{a}^{2}}-{{b}^{2}}} \right)\cdot \left( \frac{a}{a+b}+\frac{b}{a-b}-\frac{2ab}{{{a}^{2}}-{{b}^{2}}} \right)=

 

\displaystyle d)\quad \left( \frac{c+2}{2}-\frac{c-2}{c}+\frac{c-4}{2c} \right)\cdot \left( \frac{c}{c+1}+\frac{c}{c+1} \right)=