Question

Решите любые 2 номера,ПЖ!!!!

Answer 1

79.
1)
$frac{3x}{x^3-y^3}* frac{x^2+xy+y^2}{x+y}= frac{3x}{(x-y)(x^2+xy+y^2)}* frac{x^2+xy+y^2}{x+y}= frac{3x}{(x-y)(x+y)}$

2)
$frac{3}{x-y}+ frac{3x}{(x-y)(x+y)}= frac{3(x+y)+3x}{(x-y)(x+y)}= frac{3x+3y+3x}{(x-y)(x+y)}= frac{6x+3y}{(x-y)(x+y)}= frac{3(2x+y)}{(x-y)(x+y)}$

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

4)
$frac{3(x+y)}{x-y}* frac{3}{x+y}= frac{9}{x-y}$

85.
1)
$frac{x^2}{x+y}- frac{x^3}{x^2+2xy+y^2}= frac{x^2}{x+y}- frac{x^3}{(x+y)^2}= frac{x^2(x+y)-x^3}{(x+y)^2}= frac{x^3+x^2y-x^3}{(x+y)^2}= \ = frac{x^2y}{(x+y)^2}$

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

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

4)
$- frac{x^2}{x+y}- frac{x(y-x)}{x+y}= frac{-x^2-xy+x^2}{x+y}=- frac{xy}{x+y}$