Quadratic Factors in the Denominator

This is when there is a non - reducible quadratic factor in the denominator and when the degree of the denominator is greater than the degree of the numerator.

Example 1

Express as partial fractions

Step One

This expression can be written as

So

Step Two

When x = -2

20-8+4=A(8)

A=2

When x = 0

4=4A+C(2)

C=-2

Step Three

Equating co - efficients of x²

5=A+B

B=3

So the answer is