Question

Упростите выражение, 10 класс!!

Answer 1

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

$1(frac{y+2}{y^{2}-y-6}-\frac{y}{y^{2}-6y+9 })^{-1} =(\frac{y+2}{(y-3)(y+2)}-\frac{y}{(y-3)^{2} })^{-1} =(\frac{(y+2)(y-3)-y(y+2)}{(y+2)(y-3)^{2}})^{-1}=(\frac{(y+2)(y-3-y)}{(y+2)(y-3)^{2}})^{-1}=(\frac{-3}{(y-3)^{2}})^{-1}=-\frac{(y-3)^{2}}{3}\\\\2)-\frac{(y-3)^{2}}{3}:(3y-9)^{2}=-\frac{(y-3)^{2}}{3}*\frac{1}{9(y-3)^{2}}=-\frac{1}{27}$