Question

упростите выражение:

Answer 1

1)
$( \frac{1}{x+y} - \frac{x}{y^2+xy} ) * (\frac{y^2}{x^3-xy^2} - \frac{y}{x^2-xy} ) = \\ \\ = ( \frac{1}{x+y} - \frac{x}{y(x+y)} ) * (\frac{y^2}{x^2(x-y)} - \frac{y}{x(x-y)} ) = \\ \\ = \frac{1*y -x}{y(x+y)} * \frac{y^2-y*x}{x^2(x-y)} = \frac{-(x-y)*y(y-x)}{y(x+y)*x^2(x-y)} = \frac{-1 * 1(y-x)}{1*(x+y)*x^2*1} = \\ \\ = \frac{x-y}{x^2(x+y)} = \frac{x-y}{x^3+x^2y}$

2)
$( \frac{b}{a^2-ab } - \frac{1}{a-b} ) :( \frac{a+b}{a^2-ab} - \frac{b}{ab-b^2} ) = \\ \\ =( \frac{b}{a(a-b) } - \frac{1}{a-b} ) :( \frac{a+b}{a(a-b)} - \frac{b}{b(a-b)} ) = \\ \\ = \frac{b - 1*a}{a(a-b) }: \frac{(a+b)*b - b*a}{ab(a-b)} = \frac{b-a}{a(a-b)} : \frac{b*(a+b-a)}{ab(a-b)} = \\ \\ = \frac{-(a-b)}{a(a-b)} : \frac{b*b}{ab(a-b)} = - \frac{1}{a} : \frac{b}{a(a-b)} = \\ \\ = - \frac{1}{a} * \frac{a(a-b)}{b} = -\frac{a-b}{b} =$
$\frac{b-a}{b} = \frac{b}{b} - \frac{a}{b} = 1 - \frac{a}{b}$