Linear Factors in the Denominator

This is when you take a single fraction and split it into 2 or more fractions.

Example 1

Split      into partial fractions

Step One

First fully factorise the denominator

This gives

Step Two

Where there are only linear fractions in the denominator, and where the degree of the denominator is greater than the degree of the numerator the partial fractions are of the form

      where A and B are constants.

So

Step Three

We can find A and B by substituting values of x.

When x = 1

6 = 3A

A = 2      Note that this value of x eliminates the B's from the equation.

When x = -2

-10+1=B(-3)

B=3

So