Question

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

Answer 1

First, factor the numerator: `(x^2 + x - 2)`= (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 = ((x - 1)(x - 2))/[(x - 1)(x + 1)(x - 2)(x + 2)]`

`= (1)/((x + 1)(x + 2)).`