# Division of Algebraic Expressions

So far, we have learnt how to add and subtract algebraic expressions. Also how to multiply algebraic expressions. Now, we have to learn in this section how to divide one algebraic expression by another.

We know that gives . Similarly we follow the division of algebraic expressions.

Example :

Division of a monomial by another monomial:

Example

Divide

Solution

Division of a polynomial by a monomial:

There are two ways to divide a polynomial by a monomial. The first method by removing the common factor in the numerator and then dividing by the given monomial. Another method is by dividing each term in the numerator by the given monomial.

Example : Consider the division of the trinomial by the monomial 2t.

First method:

. Here is common in each term. Separating from each term we get.

Second method:

We can also divide each term of the trinomial by the monomial using cancellation method.

Example

Divide by 6
abc using both the methods.

Solution

First method: By taking out the common factor

Therefore

Second method:

Using cancellation method,

Division of Polynomial by another Polynomial:

While dividing a polynomial by another polynomial, the dividend should be written as the factor of the divisor.

Example

Solution

Example

Divide

Solution

Example

Divide:

Solution

Dividend

Thus