# How do you express 1/(s+1)^2 in partial fractions?

May 7, 2016

$\frac{1}{s + 1} ^ 2$ is already in its partial fractions form.

#### Explanation:

Partial fractions of $\frac{1}{s + 1} ^ 2$ will be of type

$\frac{1}{s + 1} ^ 2 = \frac{A}{s + 1} + \frac{B}{s + 1} ^ 2$

= $\frac{A \left(s + 1\right) + B}{s + a} ^ 2$

or $\frac{1}{s + 1} ^ 2 = \frac{A s + A + B}{s + a} ^ 2$

Equating coefficients of numerator, we have $A = 0$ and $A + B = 1$ or $B = 1$.

Hence $\frac{1}{s + 1} ^ 2 = \frac{0}{s + 1} + \frac{1}{s + 1} ^ 2$

or $\frac{1}{s + 1} ^ 2 = \frac{1}{s + 1} ^ 2$

It is apparent that $\frac{1}{s + 1} ^ 2$ is already in its partial fractions form.