# How do you express (-2x-3)/(x^2-x)  in partial fractions?

Feb 20, 2016

$\frac{3}{x} - \frac{5}{x - 1}$

#### Explanation:

To write algebraic expression (−2x−3)/(x^2−x),

we first factorize (x^2−x) i.e. x(x−1).

Hence partial fractions will be of he type

$\frac{A}{x} + \frac{B}{x - 1}$ or $\frac{A x - A + B x}{x \left(x - 1\right)}$ or

$\frac{\left(A + B\right) x - A}{x \left(x - 1\right)}$

Hence $A + B = - 2$

and $- A = - 3$ i.e. $A = 3$ and $B = - 5$

Hence partial fractions are

$\frac{3}{x} - \frac{5}{x - 1}$