Question

Упростите выражение и вычислите

($frac{5}{x-y} -frac{5x}{y^{2}-x^{2}}$)×$frac{x^{2}+2xy+y^{2}}{10x+5y}$ , при x=3,5 , y= -0,5 .

Answer 1

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

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