Упростите выражение и вычислите ()× , при x=3,5 , y= -0,5 .

$\displaystyle \bigg( \frac{5}{x-y}- \frac{5x}{y^2-x^2}\bigg)\cdot \frac{x^2+2xy+y^2}{10x+5y}=\\ \\ =\bigg( \frac{-5}{y-x}- \frac{5x}{(y-x)(y+x)}\bigg)\cdot \frac{(x+y)^2}{5(2x+y)} =\\ \\ \\ = \frac{-5x-5y-5x}{(y-x)(x+y)} \cdot \frac{(x+y)^2}{5(2x+y)}= \frac{5(-5y-10x)(x+y)^2}{(y-x)(x+y)5(2x+y)}= \\ \\ \\ = \frac{5(y+2x)(x+y)}{(x-y)(2x+y)} = \frac{5(x+y)}{x-y}$

Если х=3,5 и у=-0,5, то $\displaystyle \frac{5(x+y)}{x-y} = \frac{5\cdot(3.5-0.5)}{(3.5+0.5)}= \frac{5\cdot 3}{4} =3.75$