Question

Aratati ca ($\frac{2}{x+1}$ + $\frac{x}{1- x^{2} }$ - $\frac{3x+6}{ x^{2}+x-2}$) : $\frac{1}{1-x}$= $\frac{2x+5}{x+1}$

Answer 1

$E= (\frac{2}{x+1}+ \frac{x}{(1-x)(1+x)}- \frac{3(x+2)}{(x+2)(x-1)}): \frac{1}{1-x} \\ E= (\frac{2}{x+1}+ \frac{x}{(1-x)(1+x)}- \frac{3}{(x-1)}): \frac{1}{1-x} \\ E= (\frac{2}{x+1}+ \frac{x}{(1-x)(1+x)}+ \frac{3}{(1-x)}): \frac{1}{1-x} \\ E= \frac{2-2x+x+3x+3}{(1-x)(1+x)}\cdot (1-x) \\ E= \frac{2x+5}{1+x}=\frac{2x+5}{x+1}$