# How do you express #(x^2 - 3x) / ((x-1)(x+2))# in partial fractions?

##### 1 Answer

#### Explanation:

Firstly we must **determine** whether this type of fraction is **proper fraction or improper fraction.**

When we multiply the denominator of the fraction, the answer will be;

It is an **improper fraction** because the **denominator** (lower side of the fraction) is **greater or the same as the numerator** (upper side of the fraction, in terms of **unknown power**.

By then, to express it in partial fraction, we need to **change it into proper fraction** , which is by **long division**;

And we get the **proper fraction** of;

Until then, we can solve for the **partial fraction** by **expressing form of the rational function into form of the partial fraction** ;

We need to **find the exact value of unknown A and B.**

**Equalize the denominator** and we get;

**Cancel out the denominator** on both side;

**Relate both side of equation in terms of unknown power** by which;

In terms of unknown

**equation**

In terms of unknown **real number**

**equation**

From equation

**equation**

Substitute **equation** **equation**

Substitute **equation**

**Replace all the unknown in the partial fraction** and we will get;