Question

Помогите пожалуйста!​

Answer 1

1)

$(\frac{x}{y} +\frac{y}{x} )*\frac{x^{2}y^{2}}{x^{2}+y^{2}} -xy=( \frac{x^{2}}{xy} +\frac{y^{2}}{xy} )*\frac{x^{2}y^{2}}{x^{2}+y^{2}} -xy=\frac{x^{2}+y^{2}}{xy} *\frac{x^{2}y^{2}}{x^{2}+y^{2}} -xy=xy-xy=0$

2)

$(\frac{1}{a-b} -\frac{1}{a+b} )*\frac{2a+2b}{b} =\frac{a+b-a+b}{(a-b)(a+b)} *\frac{2(a+b)}{b} =\frac{2b}{(a-b)(a+b)} *\frac{2(a+b)}{b} =\frac{4}{a-b}$

3)

$\frac{2}{x-1} -\frac{10}{x-1} :\frac{10}{x^{2}-1} -\frac{x+1}{x-1} =\frac{2}{x-1} -\frac{10}{x-1} *\frac{(x-1)(x+1)}{10} -\frac{x+1}{x-1} =\frac{2}{x-1}-(x+1)-\frac{x+1}{x-1} =\\\\=\frac{2}{x-1}-x-1-\frac{x+1}{x-1} =\frac{2-x^{2}+1-x+1-x-1}{x-1} =\frac{-x^{2}-x+2}{x-1} =\frac{-x^{2}+x-2x+2}{x-1} =\frac{-x(x-1)-2(x-1)}{x-1} =\\\\=\frac{(-x-2)(x-1)}{x-1} =-x-2$