How to Multiply, Divide, Simplify Rational Expressions
Examples With Solutions

How to multiply, divide and simplify rational expressions? Grade 11 examples are presented along with detailed solutions and more questions with detailed Solutions and explanations are included.
If you have difficulties in multiplying, dividing and simplifying fractions and rational expressions, this tutorial will help you overcome those difficulties on the condition that you understand each step involved in solving these questions and also spend more time practicing if needed. I will present the examples below with more challenging questions as you walk through the tutorial. You need to understand each step!
An online calculator to simplify rational expressions is included and may be used to check results.


How to multiply, divide and simplify rational expressions?

We multiply two rational expressions by multiplying their numerators and denominators as follows:
1) multiply rational expressions
We divide two rational expressions by multiplying the first rational expression by the reciprocal of the second rational expression as follows:
2) divide rational expressions

Example 1

Multiply and simplify: simplify expressions example 1
Solution:
Apply the multiplication rule (see above)
solution to part 1 example 1
Factor
solution to part 2 example 1
Simplify
solution to part 3 example 1

Example 2

Multiply and simplify: simplify expressions example 2
Solution:
Apply the multiplication rule.
solution to part 1 example 2
Factor
solution to part 2 example 2
Simplify
solution to part 3 example 2

Example 3

Multiply and simplify: simplify expressions example 3.
Solution:
Multiply numerators and denominators (multiplication rule)
solution to part 1 example 3
Factor the two terms in the denominator: 4 x 2 - 49 y 2 = (2x -7y)(2x + 7y) and x 2 - 1 = (x - 1)(x + 1).
solution to part 2 example 3
Simplify
solution to part 3 example 3

Example 4

Divide and simplify: simplify expressions example 4.
Solution:
The division of two rational expressions is done by multiplying the first rational expression by the reciprocal of the second rational expression as follows (see divison rule above). Hence
solution to part 1 example 4
Multiply numerators and denominators (multiplication rule) but do not expand as we might be able to simplifty.
solution to part 2 example 4
Simplify
solution to part 3 example 4

Example 5

Divide and simplify: simplify expressions example 5.
Solution:
The division of two rational expressions is done by multiplying the first by the reciprocal of the second as follows (see divison rule above). Hence
solution to part 1 example 5
Multiply numerators and denominators (multiplication rule) but do not expand.
solution to part 2 example 5
Factor the terms included in the numerator and denominator (if possible):
solution to part 3 example 5
and use the factored form in the rational expression to simplify
solution to part 4 example 5

Example 6

Divide and simplify: simplify expressions example 6.
Solution:
We first convert (x - 2) into a rational expression. Hence
solution to part 1 example 6
The division of two rational expressions is done by multiplying the first by the reciprocal of the second as follows (see divison rule above). Hence
solution to part 2 example 6
Multiply numerators and denominators (multiplication rule) but do not expand.
solution to part 3 example 6
Factor the terms - 2 x + 4 included in the numerator as follows:
- 2 x + 4 = -2(x - 2)
and use - 2 x + 4 in factored form in the rational expression to simplify
solution to part 4 example 6

More Questions: Multiply and/or divide and simplify the given rational expressions

Detailed Solutions and explanations to these questions.
questions
Detailed Solutions and explanations to these questions.

More References and links

Rational Expressions
High School Maths (Grades 10, 11 and 12) - Free Questions and Problems With Answers
Middle School Maths (Grades 6, 7, 8, 9) - Free Questions and Problems With Answers
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