Question

Решите пожалуйста,НУЖНО ПОЛНОЕ РЕШЕНИЕ,заранее СПАСИБО ВАМ;)

Answer 1

$frac{x^2}{x^2+2xy+y^2} :( frac{x}{x+y}- frac{xy}{y^2-x^2} )= frac{x^2}{(x+y)^2} : frac{x(x-y)+xy}{(x-y)(x+y)} = frac{x^2}{(x+y)^2} cdot frac{(x-y)(x+y)}{x^2-xy+xy} = \ frac{x^2(x-y)(x+y)}{x^2(x+y)^2}= frac{x-y}{x+y}$

Answer 2

x^2/(x^2+2xy+y^2) : (x/(x+y) - xy/(y^2-x^2))=
1) (x/(x+y) - xy/(y^2-x^2)) = (x/(x+y) - xy/((y-x)(y+x))= (x(y-x)-xy)/((x-y)(x+y))= (xy-x^2-xy)/((y-x)(y+x)) = -x^2/((y-x)(y+x))
2) x^2/(x^2+2xy+y^2) : (-x^2)/((y-x)(y+x)) = x^2/(x^2+2xy+y^2) * ((y-x)(y+x))/(-x^2) = x^2((y-x)(y+x))/((x^2+2xy+y^2)(-x^2)) = -(y-x)/(x+y)= (x-y)/(x+y)