Question

Упростить выражения! Пожалуйста!!

Answer 1

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

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