Partial fractions of higher degree numerators. Here I talk about partial fractions of higher degree numerators. That means the expressions with higher degree numerators.

My aim will be to reduce its degree first. Then I will try to get partial fractions of the expression.

You can also check out how to * determine the degrees of the numerator and the denominator of any expression*.

Let me give you a few examples.

### Partial fractions of higher degree numerators with examples

##### Example 1

Write the following expression into the partial fraction form:

.

##### Solution

Here the given expression is:

That means the denominator is

So, I can say that the degree of the numerator is 3. The denominator’s degree is 2.

This means the numerator’s degree is higher than that of the denominator. Therefore this expression has a higher degree numerator.

So, my first job is to reduce the degree of the numerator.

##### Step 1

First of all, I’ll divide the numerator by the denominator.

So I can rewrite the expression as

Now

one is

the other is

The first part cannot be reduced any more.

But I can still reduce the second part. So let’s start then.

##### Step 2

Here I start with the factorisation. Then I use the assumptions like

Now I have the same denominator on both left hand and right hand sides.

Therefore I can say,

I can compare the coefficients of

Thus I get

(1)

I can also compare constants on both sides. From that I have

(2)

From equation (1), I have

Next substitute this value of

Then I get

Now I substitute this value of

Therefore I have

So the partial fraction of

Hence I can conclude that the partial fraction of

This is the solution to the given example.

Dear friends, this is the end of today’s post. Thank you very much for reading this. Please let me know how you feel about it. Soon I will be back again with a new post. Till then, bye, bye!!

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