3. Division of Algebraic Expressions

Our first examples involve simplifying and canceling.

Example 1

Example 2

Simplify math formula

Answer

Example 3

Simplify math formula

Answer

Dividing by a Fraction

Recall the following when dividing algebraic expressions.

The reciprocal of a number x, is .

For example, the reciprocal of 5 is and the reciprocal of is .

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

For example, math formula

Example 4

Simplify

Answer

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:

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

23 divided by 13 = 1 with reminder 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.

logn division

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

We use a similar technique for long division in algebra.

Example 6 - Algebraic Long Division

Simplify (3x² - 11x − 4) ÷ (x− 4)

Answer

Here is a LiveMath document which does it in one step. You can change things to see the effect. Mostly you will get a remainder of some sort, just like you do when dividing numbers.

LIVEMath

Example 7

Simplify math formula

Answer

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

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