Složené lomené výrazy – Příklady z matematiky

1) Zjednoduš:

$\displaystyle a)\quad \cfrac{\cfrac{1}{n}+\cfrac{1}{m}}{\cfrac{1}{mn}}=$

$\displaystyle b)\quad \cfrac{\cfrac{6{{u}^{2}}}{5{{v}^{3}}}}{4{{u}^{2}}v}=$

$\displaystyle c)\quad \cfrac{\cfrac{ax+ay}{xy}}{\cfrac{x+y}{x}}=$

$\displaystyle d)\quad \cfrac{\cfrac{a+b}{a-b}}{{{a}^{2}}+2ab+{{b}^{2}}}=$

$\displaystyle e)\quad \cfrac{x+y}{x-\cfrac{{{y}^{2}}}{x}}=$

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

2) Zjednoduš:

$\displaystyle a)\quad \cfrac{\cfrac{a}{{{a}^{2}}-4}}{\cfrac{{{a}^{2}}}{a+2}}=$

$\displaystyle b)\quad \cfrac{z-\cfrac{4}{z}}{z+2}=$

$\displaystyle c)\quad \cfrac{\cfrac{1}{p}+\cfrac{1}{q}}{\cfrac{p+q}{pq}}=$

$\displaystyle d)\quad \cfrac{\cfrac{1+h}{2k}}{\cfrac{{{h}^{2}}-1}{5k}}=$

$\displaystyle e)\quad \cfrac{\cfrac{{{u}^{2}}-{{v}^{2}}}{{{\left( u+v \right)}^{2}}}}{\cfrac{4u-4v}{3\left( u+v \right)}}=$

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

3) Zjednoduš:

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

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

$\displaystyle c)\quad \cfrac{\cfrac{2}{m}+\cfrac{2}{n}}{\cfrac{m+n}{mn}}=$

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

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

$\displaystyle f)\quad \cfrac{\cfrac{a}{b}-2+\cfrac{b}{a}}{\cfrac{1}{b}-\cfrac{1}{a}}=$

4) Zjednoduš:

$\displaystyle a)\quad \cfrac{\cfrac{1}{z}-\cfrac{z}{9}}{\cfrac{3+z}{3z}}=$

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

$\displaystyle c)\quad \cfrac{\cfrac{a+2}{{{a}^{2}}}}{\cfrac{1}{a}-\cfrac{4}{{{a}^{3}}}}=$

$\displaystyle d)\quad \cfrac{\cfrac{n}{4}-1+\cfrac{3}{4n}}{\cfrac{n}{2}-\cfrac{6}{n}+0,5}=$

$\displaystyle e)\quad \cfrac{1-\cfrac{u-v}{u+v}}{1+\cfrac{u+v}{u-v}}=$

$\displaystyle f)\quad \cfrac{\cfrac{x}{4}-1+\cfrac{1}{x}}{\cfrac{x+2}{x}\cdot \cfrac{x-2}{4}}=$

5) Zjednoduš:

$\displaystyle a)\quad \cfrac{1-\cfrac{2b}{a}+\cfrac{{{b}^{2}}}{{{a}^{2}}}}{\cfrac{a-b}{{{a}^{3}}}}=$

$\displaystyle b)\quad 1-\cfrac{t}{1-\cfrac{t}{t+1}}=$

➤ CMP