3. Division of Algebraic Expressions
Our first examples of division of algebraic expressions involve simplifying and canceling.
Example 1
On this page
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.
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