How do you write the partial fraction decomposition of the rational expression?

Question

(x^2) / [(x^2 + 1)(x^2 - 1)]

Answer 1

In this case, what you have is an irreducible quadratic, and a regular factorable quadratic. Your first step would be to factor the factorable quadratic.

(x^2) / [(x^2 + 1)(x^2 - 1)]

(x^2)/[(x^2 + 1)(x - 1)(x + 1)]

Whenever you have an irreducible quadratic, you will have two constants in the form Ax + B in the denominator. That's the partial fractions decomposition.

(x^2)/[(x^2 + 1)(x - 1)(x + 1)] =

(Ax + B)/(x^2 + 1) + C/(x - 1) + D/(x + 1)

Answer 2

didn't people already answer your other partial fraction decomposition question?

anyway it's A/(x+1) + B/(x-1) + Cx+D/(x^2+1) + = (x^2)/[(x^2+1)(x^2-1)]