Partial fraction of equal degree expressions. Today I will talk about a partial fraction of equal degree expressions. The partial fraction of equal degree expressions means the partial fraction of expressions where both numerators and denominators have the same degree.

### Partial fraction of equal degree expressions

In one of my earlier posts, I have already explained how to identify an expression where both the numerator and the denominator have the same degree.

Read more: Partial fraction of lower degree numerator

Let me choose a few examples.

##### Example 1

Write in partial fraction form:

.

##### Solution

Now my aim is to remove from the top. For that I can write this expression as

Now is removed from the top and is the partial fraction of .

Let me choose another example.

##### Example 2

Write in partial fraction form:

.

##### Solution

Here also my aim is to remove from the top. So I can write the expression as

Now I can say is the partial fraction of .

Now I’ll solve one more problem where both the numerator and the denominator have the degree 2.

##### Example 3

Write in partial fraction form:

.

##### Solution

In this case, I have to remove both and from the top. Like other examples above, here also I’ll start in the same way.

Now I have two components of this expression: one is 2 and the other is . I cannot decompose 2 further. But I can still break down .

Let’s look at the expression . Here numerator has a lower degree than the denominator. So I can use the same way of partial fraction decomposition.

To start with, first I’ll factorize .

Now I rewrite as .

Let me assume

where are constants.

Now I can say

.

I can compare coefficients on both sides. Therefore I have two simple equations.

(1)

and

(2)

At the next stage I’ll solve equations (1) and (2) to get the values of and . From equation (1), I can say, . I substitute this value of in equation (2) and then solve for .

For , .

Therefore the partial fraction of is .

Thus I can say the partial fraction form of is . This is the answer to the problem no 3.

Dear friends, this is the end of my today’s example. Thank you very much for reading my post. Soon I will be back with a new post on a different topic!! Till then, bye, bye.

## Leave a Reply