Question

Solve
$\frac{x+1}{2}+\frac{2}{x+1}=\frac{x+1}{3}+\frac{3}{x+1}-\frac{5}{6}(x\ne -1)$

Answer 1

$\frac{x+1}{2}+\frac{2}{x+1}=\frac{x+1}{3}+\frac{3}{x+1}-\frac{5}{6}$

$\frac{x+1}{2}-\frac{x+1}{3}=\frac{3}{x+1}-\frac{2}{x+1}-\frac{5}{6}$

$\frac{3x+3-2x-2}{6}=\frac{3-2}{x+1}-\frac{5}{6}$

$\Rightarrow \frac{x+1}{6}+\frac{5}{6}=\frac{1}{x+1}$

$\Rightarrow \frac{x+6}{6}=\frac{1}{x+1}$

$\Rightarrow x^2+7x+6=6$

$\Rightarrow x(x+7)=0$

$\Rightarrow x=0,-7$