The following is an Exact Differential Equation :-

$\displaystyle (\frac{x+y}{y-1}) dx -\frac{1}{2}(\frac{x+1}{y-1})^2dy$

Multiplied both sides with $\displaystyle 2(y-1)^2$.

Then opened $\displaystyle -(x+1)^2$ and $\displaystyle (y-1)(x+y)$.

After partial differentiation the two sides doesn't come the same whereas this whole exercise is composed of questions which areExact. And the end answer also doesn't come correct.

Is there a problem with my approach or what ?