# How do you simplify (x^2+x-2)/(x^4-5x^2+4)?

##### 1 Answer
May 28, 2015

First, factor the numerator: $\left({x}^{2} + x - 2\right)$= (x - 1)(x - 2)
Next, factor the denominator. Call X = x^2.

X^2 - 5X + 4 = (X - 1)(X - 4) = (x^2 - 1)(x^2 - 4) =

= (x - 1)(x + 1)(x - 2)(x + 2)

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

$= \frac{1}{\left(x + 1\right) \left(x + 2\right)} .$