1)      Napište, kdy má daný výraz smysl, a zkraťte:

\displaystyle a)\quad \frac{3a}{3b}=

 

\displaystyle b)\quad \frac{9u}{9{{v}^{2}}}=

\displaystyle c)\quad \frac{6p}{18{{q}^{3}}}=

 

\displaystyle d)\quad \frac{4x}{7x}=

\displaystyle e)\quad \frac{5{{r}^{2}}}{10s}=

 

\displaystyle f)\quad \frac{14m}{21{{n}^{2}}}=

\displaystyle g)\quad \frac{ax}{ay}=

 

\displaystyle h)\quad \frac{4z}{10z}=


 

2)      Určete, kdy má výraz smysl a zkraťte:

\displaystyle a)\quad \frac{{{x}^{3}}}{{{x}^{5}}}=

 

\displaystyle b)\quad \frac{2{{c}^{6}}}{5{{c}^{3}}}=

\displaystyle c)\quad \frac{3{{k}^{2}}}{6k}=

 

\displaystyle d)\quad \frac{2{{s}^{3}}}{5s}=

\displaystyle e)\quad \frac{5b}{20ab}=

 

\displaystyle f)\quad \frac{10{{m}^{2}}}{2m}=

\displaystyle g)\quad \frac{{{r}^{2}}x}{r{{x}^{2}}}=

 

\displaystyle h)\quad \frac{7u}{{{u}^{3}}}=


 

3)      Zkraťte na základní tvar a napište, kdy má výraz smysl:

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

 

\displaystyle b)\quad \frac{5{{u}^{3}}}{7{{u}^{2}}v}=

\displaystyle c)\quad \frac{16xy}{20{{x}^{2}}z}=

 

\displaystyle d)\quad \frac{3{{u}^{2}}{{v}^{3}}}{15{{u}^{3}}{{v}^{2}}}=

\displaystyle e)\quad \frac{6p}{9{{p}^{4}}q}=

 

\displaystyle f)\quad \frac{24{{a}^{3}}{{x}^{2}}}{30a{{x}^{2}}}=

\displaystyle g)\quad \frac{2a{{b}^{2}}c}{8{{a}^{2}}b{{c}^{2}}}=

 

\displaystyle h)\quad \frac{15{{r}^{2}}{{s}^{2}}}{17r{{s}^{2}}}=


 

4)      Zkraťte na základní tvar a napište, kdy má výraz smysl:

\displaystyle a)\quad \frac{{{k}^{2}}m{{n}^{3}}}{{{k}^{2}}{{m}^{3}}{{n}^{4}}}=

 

\displaystyle b)\quad \frac{7b{{c}^{2}}}{21b{{d}^{3}}}=

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

 

\displaystyle d)\quad \frac{9{{x}^{3}}{{y}^{3}}}{{{\left( 3x{{y}^{2}} \right)}^{2}}}=

\displaystyle e)\quad \frac{2{{a}^{3}}}{{{\left( 3ab \right)}^{2}}}=

 

\displaystyle f)\quad \frac{{{\left( 3m \right)}^{3}}n}{9{{m}^{3}}{{n}^{3}}}=

\displaystyle g)\quad \frac{{{\left( 2u \right)}^{3}}}{2{{u}^{3}}}=

 

\displaystyle h)\quad \frac{r{{\left( pq \right)}^{2}}}{{{p}^{2}}{{q}^{4}}r}=


 

5)      Zkraťte na základní tvar a napište, kdy má výraz smysl:

\displaystyle a)\quad \frac{u\left( x-1 \right)}{v\left( x-1 \right)}=

 

\displaystyle b)\quad \frac{x-2}{5x-10}=

 

\displaystyle c)\quad \frac{3a+3b}{7a+7b}=

\displaystyle d)\quad \frac{4\left( 3p+q \right)}{r\left( 3p+q \right)}=

 

\displaystyle e)\quad \frac{5m+10n}{3m+6n}=

 

\displaystyle f)\quad \frac{4{{r}^{2}}-4}{{{r}^{2}}-1}=

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

 

\displaystyle h)\quad \frac{3a-6}{6a-12}=


 

6)      Zkraťte na základní tvar a napište, kdy má výraz smysl:

\displaystyle a)\quad \frac{k+1}{{{k}^{2}}+k}=

 

\displaystyle b)\quad \frac{3{{r}^{2}}-3{{r}^{3}}}{r-{{r}^{2}}}=

 

\displaystyle c)\quad \frac{{{m}^{2}}+m}{{{m}^{2}}-m}=

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

 

\displaystyle e)\quad \frac{10rs-14rt}{20s-28t}=

 

\displaystyle f)\quad \frac{9{{z}^{3}}-27vz}{{{z}^{4}}-3v{{z}^{2}}}=

\displaystyle g)\quad \frac{4{{x}^{2}}+4x}{2xy+2x}=

 

\displaystyle h)\quad \frac{6a+2ab}{2{{a}^{2}}-4a}=

 

\displaystyle i)\quad \frac{4{{\left( x-y \right)}^{2}}}{6xy-6{{y}^{2}}}=


 

7)      Zkraťte na základní tvar a napište, kdy má výraz smysl:

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

 

\displaystyle b)\quad \frac{{{r}^{2}}-4}{r+2}=

 

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

\displaystyle d)\quad \frac{u+3}{{{u}^{2}}-9}=

 

\displaystyle e)\quad \frac{{{\left( m+n \right)}^{2}}}{mn+{{n}^{2}}}=

 

\displaystyle f)\quad \frac{{{s}^{2}}-16}{\left( s+4 \right)\cdot \left( s-4 \right)}=

\displaystyle g)\quad \frac{{{z}^{2}}-1}{az+a}=

 

\displaystyle h)\quad \frac{{{x}^{2}}+5x}{{{x}^{2}}-25}=

 

\displaystyle i)\quad \frac{r+s}{{{r}^{2}}+2rs+{{s}^{2}}}=


 

8)      Zkraťte na základní tvar a napište, kdy má výraz smysl:

\displaystyle a)\quad \frac{3p-3q}{{{\left( p-q \right)}^{2}}}=

 

\displaystyle b)\quad \frac{{{a}^{2}}+2a+1}{2a+2}=

 

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

\displaystyle d)\quad \frac{2{{h}^{2}}+6h}{4hk}=

 

\displaystyle e)\quad \frac{4pq+2{{p}^{2}}q}{2pq}=

 

\displaystyle f)\quad \frac{{{a}^{2}}c-a{{c}^{2}}}{{{a}^{2}}b{{c}^{2}}}=

\displaystyle g)\quad \frac{x{{y}^{2}}}{{{x}^{2}}y-x{{y}^{3}}}=

 

\displaystyle h)\quad \frac{{{u}^{3}}+uv}{{{u}^{4}}}=

 

\displaystyle i)\quad \frac{7a+14}{4{{a}^{2}}-16}=


 

9)      Zkraťte na základní tvar a napište, kdy má výraz smysl:

\displaystyle a)\quad \frac{3ab+5a{{b}^{2}}}{2{{a}^{2}}b}=

 

\displaystyle b)\quad \frac{4xy-2y}{2{{x}^{2}}y}=

 

\displaystyle c)\quad \frac{m+5}{25-{{m}^{2}}}=

\displaystyle d)\quad \frac{{{x}^{2}}-x}{{{x}^{2}}+x}=

 

\displaystyle e)\quad \frac{20{{a}^{2}}b}{4{{a}^{2}}bc-8{{a}^{2}}b}=

 

\displaystyle f)\quad \frac{12{{r}^{2}}{{s}^{4}}-60{{r}^{2}}{{s}^{2}}}{12{{r}^{2}}{{s}^{2}}}=

\displaystyle g)\quad \frac{x+1}{a+ax}=

 

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

 

\displaystyle i)\quad \frac{36{{a}^{2}}}{9{{a}^{3}}-36a}=