Question

Упростите выражение 2.001

Answer 1

$frac{sqrt{x}+1}{xsqrt{x}+x+sqrt{x}}:frac{1}{x^2-sqrt{x}}=frac{sqrt{x}+1}{xsqrt{x}+x+sqrt{x}}*frac{x^2-sqrt{x}}{1}=\frac{(sqrt{x}+1)(x^2-sqrt{x})}{xsqrt{x}+x+sqrt{x}}=frac{x^2sqrt{x}-x+x^2-sqrt{x}}{xsqrt{x}+x+sqrt{x}}=frac{x^2sqrt{x}-sqrt{x}+x^2-x}{xsqrt{x}+x+sqrt{x}}=frac{sqrt{x}(x^2-1)+x(x-1)}{xsqrt{x}+x+sqrt{x}}=\frac{(x-1)(sqrt{x}(x+1)+x)}{xsqrt{x}+x+sqrt{x}}=frac{(x-1)(xsqrt{x}+x+sqrt{x})}{xsqrt{x}+x+sqrt{x}}=x-1$