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Question 1

Question 2

Решите задачу:

$\frac{\sqrt{x-\sqrt{4(x-1)}}+\sqrt{x+\sqrt{4(x-1)}}}{\sqrt{x^2-4(x-1)}}\cdot (1-\frac{1}{x-1}) = \\ = \frac{\sqrt{(x-1)-2\sqrt{x-1}+1}+\sqrt{(x-1)+2\sqrt{x-1}+1}}{\sqrt{x^2-4x-4}}\cdot \frac{x-2}{x-1} = \\ = \frac{\sqrt{(x-1-1)^2}+\sqrt{(x-1+1)^2}}{\sqrt{(x-2)^2}}\cdot \frac{x-2}{x-1} = \frac{x-2+x}{x-2}\cdot \frac{x-2}{x-1} = \frac{2(x-1)}{x-1} = 2$

$(\frac{(b^{\frac{2}{3}}\sqrt[3]{a\sqrt{b}}-a^{\frac{1}{2}}\sqrt[3]{ab})^2}{\sqrt[3]{a^3\sqrt{a}}\cdot b\sqrt[6]{b}}+4)\cdot(\frac{\sqrt{a^2b}+b\sqrt{a}}{\sqrt{a}-\sqrt{b}})^{-1} = \\ = (\frac{(a^{\frac{1}{3}}b^{\frac{5}{6}}-a^{\frac{5}{6}}b^{\frac{1}{3}})^2}{a^{\frac{7}{6}}\cdot b^{\frac{7}{6}}}+4)\cdot\frac{a^{\frac{1}{2}}-b^{\frac{1}{2}}}{ab^{\frac{1}{2}}+ba^{\frac{1}{2}}} =$
$(\frac{a^{\frac{2}{3}}b^{\frac{2}{3}}(b^{\frac{1}{2}}-a^{\frac{1}{2}})^2}{a^{\frac{7}{6}}\cdot b^{\frac{7}{6}}}+4)\cdot\frac{a^{\frac{1}{2}}-b^{\frac{1}{2}}}{a^{\frac{1}{2}}b^{\frac{1}{2}}(a^{\frac{1}{2}}+b^{\frac{1}{2}})} =\\= (\frac{(b^{\frac{1}{2}}-a^{\frac{1}{2}})^2}{a^{\frac{1}{2}}\cdot b^{\frac{1}{2}}}+4)\cdot\frac{a^{\frac{1}{2}}-b^{\frac{1}{2}}}{a^{\frac{1}{2}}b^{\frac{1}{2}}(a^{\frac{1}{2}}+b^{\frac{1}{2}})} =$
$\frac{b-2b^{\frac{1}{2}}a^{\frac{1}{2}}+a+4a^{\frac{1}{2}}b^{\frac{1}{2}}}{a^{\frac{1}{2}} b^{\frac{1}{2}}}\cdot\frac{a^{\frac{1}{2}}-b^{\frac{1}{2}}}{a^{\frac{1}{2}}b^{\frac{1}{2}}(a^{\frac{1}{2}}+b^{\frac{1}{2}})} =\\= \frac{(a^{\frac{1}{2}}+b^{\frac{1}{2}})^2(a^{\frac{1}{2}}-b^{\frac{1}{2}})}{ab(a^{\frac{1}{2}}+b^{\frac{1}{2}})} = \frac{a-b}{ab}$