Problem:
$\displaystyle \frac{5x}{x-1}-3=\frac{2x+5}{x^2-1}$
Solution
$\displaystyle x=2$
$\displaystyle x=-\frac{1}{2}$
$\displaystyle \frac{5x}{x-1}-3=\frac{2x+5}{x^2-1}$
common denominator ...
$\displaystyle \frac{5x(x+1)}{(x-1)(x+1)}-\frac{3(x^2-1)}{x^2-1}=\frac{2x+5}{x^2-1}$
numerators form the equation ...
$\displaystyle 5x(x+1) - 3(x^2-1) = 2x+5 \, \, ; \, \, x \ne \pm 1$
take it from here?