Expert: Paul Klarreich - 3/3/2010

Question
Resolve the following improper fraction into partial fractions:

       x^4
------------------
(x^2 + 1)(x^2 - 1)

Answer
Questioner: Ilse
Country: South Africa
Category: Advanced Math
Private: No
Subject: Resolve fractions
Question: Resolve the following improper fraction into partial fractions:

      x^4
------------------
(x^2 + 1)(x^2 - 1)


Step 1: Since the degree of the top and bottom are equal, this is an improper fraction and you must do long division first.

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


  x^4              1
--------- = 1 + --------  = 1 plus
x^4  - 1        x^4 - 1

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

Ax + B       C        D
--------- + ------ + ------
x^2 + 1   x - 1    x + 1

Step 2: Do the standard stuff:

1. Multiply out on both sides:

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

2. Do your standard stuff as described in your textbook.