# How do you write the partial fraction decomposition of the rational expression (2x-3) / (x-1)^2?

$\frac{2 x - 3}{x - 1} ^ 2 = \frac{2}{x - 1} - \frac{1}{x - 1} ^ 2$
$\frac{2 x - 3}{x - 1} ^ 2 = \frac{A}{x - 1} + \frac{B}{x - 1} ^ 2$
$2 x - 3 = A \left(x - 1\right) + B$
$x = 1 \to - 1 = B$
Comparing coefficients of the $x$ term on both sides, we see that $A = 2$
Therefore, $\frac{2 x - 3}{x - 1} ^ 2 = \frac{2}{x - 1} - \frac{1}{x - 1} ^ 2$