Partial Fraction confusion

Question

How to solve this using partial fraction $$\frac{x^2+7}{(2x-1)(x-1)}$$

I am using $\frac{A}{2x-1}+\frac{B}{x-1}$ but not getting it

Answer 1

First perform long division: \begin{align} \frac{x^2+7}{(2x-1)(x-1)}&=\frac{1}{2}+\frac{\frac{3}{2}x+\frac{13}{2}}{(2x-1)(x-1)} \end{align} Then, put $$\frac{\frac{3}{2}x+\frac{13}{2}}{(2x-1)(x-1)}=\frac{A}{2x-1}+\frac{B}{x-1}$$

Answer 2

Hint: Subtract $-8$ and add back $8$ to $x^2+7$.