Repeated Factor in the Denominator

This is when the fraction has a repeated factor in the denominator and when the degree of the denominator is greater than the degree of the numerator.

Example 3

Express as partial fractions

Step One

In this case the partial fractions are of the form

So

Step Two

When x = 1

2(1-2-1)=C(2)

C=-2

When x = -1

2(1+2-1)=A(-2)²

A = 1

Step Three

Comparing co - efficients of x² gives

2 = A + B

2 = 1 + B

B = 1

So answer is