Question

Упростить $frac{sqrt{x}+1}{1+sqrt{x}+x}:frac{1}{x^2-sqrt{x}}$

Answer 1

$frac{sqrt{x}+1}{1+sqrt{x}+x}:frac{1}{x^2-sqrt{x}}=frac{sqrt{x}+1}{1+sqrt{x}+x} cdotfrac{x^2-sqrt{x}}{1}=frac{sqrt{x}+1}{1+sqrt{x}+x}cdotfrac{sqrt{x}((sqrt{x})^3-1)}{1}=frac{sqrt{x}+1}{1+sqrt{x}+x}cdotfrac{sqrt{x}(sqrt{x}-1)(1+sqrt{x}+x)}{1} =sqrt{x}(sqrt{x}-1)(sqrt{x}+1)=sqrt{x}(x-1)=xsqrt{x}-sqrt{x}.$