Partial fractions of higher degree numerators. Here I’ll talk about the partial fractions of higher degree numerators.

If you are looking for more in partial differentiation, do check out:

**Partial fractions of irreducible quadratic factors**

**Partial fractions of equal degree expressions**

**How to get partial fractions of repeated roots**

*Partial fractions of lower degree numerators*

Now the partial fraction of a higher degree numerator means the expression with the higher degree numerator. 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 . Also the numerator 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 is reduced to two parts:

one is and

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 on both sides.

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 in equation (2).

Then I get

Now I substitute this value of in equation (1).

Therefore I have

So the partial fraction of is .

Hence I can conclude that the partial fraction of is .

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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