3. Division of Algebraic Expressions

Our first examples of division of algebraic expressions involve simplifying and canceling.

Example 1

Simplify (3ab(4a^2b^5))/(8a^2b^3)

Example 2

Simplify (12m^2n^3)/((6m^4n^5)^2)

Example 3

Simplify (6p^3q^2-10p^2q)/(4q)

Dividing by a Fraction

Recall the following when dividing algebraic expressions.

The reciprocal of a number x, is 1/x.

For example, the reciprocal of 5 is 1/5 and the reciprocal of 1 2/3 is 3/5.

To divide by a fraction, you multiply by the reciprocal of the fraction.

For example, 3/4 -: 7/x=3/4xxx/7=(3x)/28

Example 4

Simplify

(3+1/x)/(5/x+4)

Long Division in Algebra

Before we do an example using algebra, let’s remember how to do long division with numbers first.

Example 5

Let’s do 23,576 divided by 13.

We can write this as a fraction:

23576/13

Now, to divide this, (assuming we do not have a calculator) we could proceed as follows.

23 divided by 13 = 1 with remainder 10.

We bring the 5 (the next number after 3) down.

Now we have

105 divided by 13 is 8 with remainder 1

We continue until we get to the last number, 6.

Our result means that the answer is 1,813 with remainder 7, or:

23576/13=1813 7/13

We use a similar technique for long division in algebra.

Example 6 - Algebraic Long Division

Simplify (3x^2-11x-4)-:(x-4)

Example 7

Simplify (6x^2+6+7x)/(2x+1)

You can see how algebraic long division is used in a later section, Remainder and Factor Theorems.

Didn't find what you are looking for on this page? Try search:

Online Algebra Solver

This algebra solver can solve a wide range of math problems. (Please be patient while it loads.)

Play a math game.

(Well, not really a math game, but each game was made using math...)

Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!

Given name: * required

Family name:

email: * required

See the Interactive Mathematics spam guarantee.