Question

Ребят,пожалуйста помогите (смотрите вложение)

Answer 1

1)$(\frac{a+1}{2a-2}-\frac{1}{a+1})(\frac{2a+2}{a+2})=(\frac{(a+1)(a+1)}{2(a-1)(a+1)}-\frac{2(a-1)}{2(a+1)(a-1)})(\frac{2a+2}{a+2})=(\frac{a^2+2a+1}{2(a^2-1)}-\frac{2a-2}{2(a^2-1)})(\frac{2a+2}{a+2})=\frac{a^2+3}{2(a-1)(a+1)}(\frac{2(a+1)}{a+2})=\frac{a^2+3}{(a-1)(a+2)}=\frac{a^2+3}{a^2+a-2}$

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

3)$(\frac{c+d}{c}-\frac{2c}{c-d})*\frac{d-c}{c^2+d^2}=(\frac{(c+d)(c-d)}{c(c-d)}-\frac{2c^2}{c(c-d)})*\frac{d-c}{c^2+d^2}=\frac{c^2-d^2-2c^2}{c(c-d)}*\frac{d-c}{c^2+d^2}=\frac{-d^2-c^2}{-c(d-c)}*\frac{d-c}{c^2+d^2}=\frac{d^2+c^2}{c}*\frac{1}{c^2+d^2}=\frac{1}{c}$