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

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Answer 1 · 2015-05-28T03:14:05

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)#

$y = ((x - 1)(x - 2))/[(x - 1)(x + 1)(x - 2)(x + 2)]$

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

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