Решение №16887: \(\frac{\left ( pq^{-1}+1 \right )^{2}}{pq^{-1}-p^{-1}q}\cdot \frac{p^{3}q^{-3}-1}{p^{2}q^{-2}+pq^{-1}+1}:\frac{p^{3}q^{-3}+1}{pq^{-1}+p^{-1}q-1}=\frac{\left ( p+q \right )^{2}}{q^{2}}\cdot \frac{pq}{p^{2}-q^{2}}\cdot \frac{p^{3}-q^{3}}{q^{3}}\cdot \frac{q^{2}}{p^{2}+pq+q^{2}}:\left ( {\frac{p^{3}-q^{3}}{q^{3}}}{}\cdot \frac{pq}{p^{2}-pq+q^{2}} \right )=\frac{\left ( p+q \right )^{2}p}{q\left ( p+q \right )\left ( p-q \right )}\cdot \frac{\left ( p-q \right )\left ( p^{2}+pq+q^{2} \right )}{q\left ( p^{2}+pq+q^{2} \right )}:\left ( \frac{\left ( p+q \right )\left ( p^{2}-pq+q^{2} \right )p}{q^{2}\left ( p^{2}-pq+q^{2} \right )} \right )=\frac{p\left ( p+q \right )}{q^{2}}:\frac{p\left ( p+q \right )}{q^{2}}=1\)

Ответ: 1

Решение №16888: \(\frac{\sqrt{\sqrt{a}-\sqrt{b}+\sqrt[4]{b}}\cdot \sqrt{\sqrt{a}-\sqrt{b}-\sqrt[4]{b}}}{\sqrt{\left ( 1+\sqrt{\frac{b}{a}} \right )^{2}-4\sqrt{\frac{b}{a}}-\frac{\sqrt{b}}{a}}}=\frac{\sqrt{\left ( \sqrt{a}-\sqrt{b}+\sqrt[4]{b} \right )\left ( \sqrt{a}-\sqrt{b}-\sqrt[4]{b} \right )}}{\sqrt{\frac{a-2\sqrt{ab}+b-\sqrt{b}}{a}}}=\sqrt{a}=\sqrt{1.21}=1.1\)

Ответ: 1.1

Решение №16889: \(\frac{8-n}{2+\sqrt[3]{n}}:\left ( 2+\frac{\sqrt[3]{n^{2}}}{2+\sqrt[3]{n}} \right )-\left ( \sqrt[3]{n}+\frac{2\sqrt[3]{n}}{\sqrt[3]{n}-2} \right )\cdot \frac{4-\sqrt[3]{n^{2}}}{\sqrt[3]{n^{2}}+2\sqrt[3]{n}}=\frac{\left ( 2-\sqrt[3]{n} \right )\left ( 4+2\sqrt[3]{n}+\sqrt[3]{n^{2}} \right )}{2+\sqrt[3]{n}}\cdot \frac{2+\sqrt[3]{n}}{4+2\sqrt[3]{n}+\sqrt[3]{n^{2}}}+\frac{\sqrt[3]{n^{2}}}{2-\sqrt[3]{n}}\cdot \frac{2-\sqrt[3]{n}}{\sqrt[3]{n}}=2-\sqrt[3]{n}+\sqrt[3]{n}=2\)

Ответ: 2

Решение №16890: \(\frac{\left ( \sqrt{x}+2 \right )\left ( \frac{2}{\sqrt{x}} -1\right )-\left ( \sqrt{x}-2 \right )\left ( \frac{2}{\sqrt{x}}+1 \right )-\frac{8}{\sqrt{x}}}{\left ( 2-\sqrt{x+2} \right ):\left ( \sqrt{\frac{2}{x}+1}-\frac{2}{\sqrt{x}} \right )}=\frac{\frac{\left ( \sqrt{x}+2 \right )\left (2- \sqrt{x} \right )}{\sqrt{x}}-\frac{\left ( \sqrt{x}+2 \right )\left (2+ \sqrt{x} \right )}{\sqrt{x}}-\frac{8}{\sqrt{x}}}{\left ( 2-\sqrt{x+2} \right ):\left ( \frac{\sqrt{2+x}}{\sqrt{x}}}-\frac{2}{\sqrt{x} \right )}=2\)

Ответ: 2

Решение №16891: \(\frac{\sqrt{x-2\sqrt{2}}}{\sqrt{x^{2}}-4x\sqrt{2}+8}-\frac{\sqrt{x+2\sqrt{2}}}{\sqrt{x^{2}}+4x\sqrt{2}+8}=\frac{\sqrt{x-2\sqrt{2}}}{\sqrt{\left ( x-2\sqrt{2} \right )^{2}}}-\frac{\sqrt{x+2\sqrt{2}}}{\sqrt{\left ( x+2\sqrt{2} \right )^{2}}}=\frac{1}{\sqrt{x-2\sqrt{2}}}-\frac{1}{\sqrt{x+2\sqrt{2}}}=\frac{\sqrt{3+2\sqrt{2}}-\sqrt{3-2\sqrt{2}}}{\sqrt{9-8}}=\sqrt{3+2\sqrt{2}}-\sqrt{3-2\sqrt{2}}=\sqrt{\left ( \sqrt{3+2\sqrt{2}}-\sqrt{3-2\sqrt{2}} \right )^{2}}=\sqrt{6-2\sqrt{9-8}}=\sqrt{6-2}=\sqrt{4}=2\)

Ответ: 2

Решение №16892: \(\frac{8-m}{\sqrt[3]{m}+2}:\left ( 2+\frac{\sqrt[3]{m^{2}}}{\sqrt[3]{m}+2} \right )+\left ( \sqrt[3]{m}+\frac{2\sqrt[3]{m}}{\sqrt[3]{m}-2} \right )\cdot \frac{\sqrt[3]{m^{2}-4}}{\sqrt[3]{m^{2}}+2\sqrt[3]{m}}=\frac{\left ( 2-\sqrt[3]{m} \right )\left ( 4+2\sqrt[3]{m}+\sqrt[3]{m^{2}} \right )}{\sqrt[3]{m}+2}\cdot \frac{\sqrt[3]{m}+2}{4+2\sqrt[3]{m}+\sqrt[3]{m^{2}}}+\sqrt[3]{m}=2-\sqrt[3]{m}+\sqrt[3]{m}=2\)

Ответ: 2

Решение №16893: \(\frac{\sqrt{a^{2}-b+\sqrt{c}}\sqrt{a-\sqrt{b+\sqrt{c}}}\sqrt{a+\sqrt{b+\sqrt{c}}}}{\sqrt{\frac{a^{3}}{b}-2a+\frac{b}{a}-\frac{c}{ab}}}=\frac{\sqrt{a^{2}-b+\sqrt{c}}\sqrt{\left ( a-\sqrt{b+\sqrt{c}} \right )\left ( a+\sqrt{b+\sqrt{c}} \right )}}{\sqrt{\frac{a^{4}+2a^{2}b+b^{2}-c}{ab}}}=\frac{\sqrt{a^{2}-b+\sqrt{c}}\sqrt{a^{2}-\left ( \sqrt{b+\sqrt{c}} \right )^{2}}}{\sqrt{\frac{\left ( a^{2}-b \right )^{2}-c}{ab}}}=\frac{\sqrt{\left ( a^{2}-b+\sqrt{c} \right )\left ( a^{2}-b-\sqrt{c} \right )}}{\frac{\sqrt{\left ( a^{2}-b+\sqrt{c} \right )\left ( a^{2}-b-\sqrt{c} \right )}}{\sqrt{ab}}}=\sqrt{ab}=\sqrt{4.8*1.2}=\sqrt{5.76}=2.4\)

Ответ: 2.4

Решение №16894: \(\frac{\left ( a-b \right )^{3}\left ( \sqrt{a}+\sqrt{b} \right )^{-3}+2a\sqrt{a}+b\sqrt{b}}{a\sqrt{a}+b\sqrt{b}}+\frac{3\left ( \sqrt{ab}-b \right )}{a-b}=\frac{\left ( a-b \right )^{3}+\left ( 2a\sqrt{a}+b\sqrt{b} \right )\left ( \sqrt{a}+\sqrt{b} \right )^{3}}{\left ( \sqrt{a}+\sqrt{b} \right )^{3}\left ( a\sqrt{a}+b\sqrt{b} \right )}+\frac{3\sqrt{b}}{\sqrt{a}+\sqrt{b}}=\frac{3\left ( a^{3}+3a^{2}b+3ab^{2}+b^{3}+3a^{2}\sqrt{ab}+3b^{2}\sqrt{ab}+2ab\sqrt{ab} \right )}{a^{3}+3a^{2}b+3ab^{2}+b^{3}+3a^{2}\sqrt{ab}+3b^{2}\sqrt{ab}+2ab\sqrt{ab}}=3\)

Ответ: 3

Решение №16895: \(\left ( \frac{x+2y}{8y^{3}\left ( x^{2}+2xy+2y^{3} \right )}-\frac{\left ( x-2y \right ):8y^{2}}{x^{2}-2xy+2y^{2}} \right )+\left ( \frac{y^{-2}}{4x^{2}-8y^{2}}-\frac{1}{4x^{2}y^{2}+8y^{4}} \right )=\frac{\left ( x+2y \right )\left ( x^{2}+2y^{2}-2xy \right )-\left ( x-2y \right )\left ( x^{2}+2y^{2}+2xy \right )}{8y^{3}\left ( x^{2}+2y^{2}+2xy \right )\left ( x^{2}+2y^{2}-2xy \right )}+\frac{x^{2}+2y^{2}-x^{2}+2y^{2}}{4y^{2}\left ( x^{2}-2y^{2} \right )\left ( x^{2}+2y^{2} \right )}=\frac{1}{x^{4}+4y^{4}}+\frac{1}{x^{4}+4y^{4}}=\frac{2x^{4}}{x^{8}-16y^{8}}=\frac{2\left ( \sqrt[4]{6} \right )^{4}}{\left ( \sqrt[4]{6} \right )^{8}-16\left ( \sqrt[8]{2} \right )^{8}}=\frac{12}{4}=3\)

Ответ: 3

Решение №16896: \(\frac{2\left ( a+\left ( a+1 \right )+\left ( a+2 \right ) \right )+...+2}{a^{2}+3a+2}+\frac{6\left ( a^{\frac{1}{2}}+b^{\frac{1}{2}} \right )}{\left ( a-b \right )^{0.6}\left ( a+2 \right )}\cdot \left ( \left ( a^{\frac{1}{2}}-b^{\frac{1}{2}} \right )\left ( a-b \right )^{-\frac{2}{5}} \right )^{-1}=\frac{3a\left ( a+1 \right )}{\left ( a+2 \right )\left ( a+1 \right )}+\frac{6\left ( \sqrt{a}+\sqrt{b} \right )}{\sqrt[5]{\left ( a-b \right )^{3}}\left ( a+2 \right )}:\frac{1}{\left ( \sqrt{a}-\sqrt{b} \right )\sqrt[5]{\left ( a-b \right )^{-2}}}=\frac{3a}{a+2}+\frac{6\left ( a-b \right )}{\left ( a+2 \right )\sqrt[5]{\left ( a-b \right )^{5}}}=\frac{3a}{a+2}+\frac{6}{a+2}=\frac{3a+6}{a+2}=3\)

Ответ: 3