# How do you express x^3/[x(x^2+2x+1)] in partial fractions?

Apr 13, 2016

${x}^{3} / \left(x \left({x}^{2} + 2 x + 1\right)\right) = 1 - \frac{2}{x + 1} + \frac{1}{x + 1} ^ 2$

#### Explanation:

This one is relatively simpler and need for detailed solution as given here, does not arise.

${x}^{3} / \left(x \left({x}^{2} + 2 x + 1\right)\right) = {x}^{2} / \left({x}^{2} + 2 x + 1\right) = \frac{{x}^{2} + 2 x + 1 - \left(2 x + 1\right)}{{x}^{2} + 2 x + 1}$

= $1 - \frac{2 x + 1}{x + 1} ^ 2$

= $1 - \frac{2 x + 2 - 1}{x + 1} ^ 2$

= $1 - \frac{2 \left(x + 1\right)}{x + 1} ^ 2 + \frac{1}{x + 1} ^ 2$ or

= $1 - \frac{2}{x + 1} + \frac{1}{x + 1} ^ 2$