How To Simplify Rational Expressions? - Examples With Detailed Solutions

How to simplify rational expressions? Grade 11 examples are presented along with detailed solutions and full explanations. More questions with answers at the bottom of the page are also included.

How to simplify rational expressions?

How to simplify rational expressions? The rules of addition, subtraction, multiplication and division of rational expressions are used to simplify complex expressions.

Rational expressions with the same denominator are added or subtracted as follows:

add/subtract rational expressions


Rational expressions are multplied as follows:

multiply rational expressions


We divide two rational expressions by multiplying the first rational expression by the reciprocal of the second rational expression as follows:

divide rational expressions

If you have difficulties in simplifying rational expressions, review the tutorials in How to Add, Subtract and Simplify Rational Expressions and How to multiply, divide and simplify rational expressions and then start the present tutorial. The examples with detailed solutions and explanations in this tutorials will help you overcome any difficulties in simplifying rational expressions on the condition that you understand every step involved in solving these questions and also spend more time practicing if needed. I will present the examples below starting with fractions first and then with rational expressions, with more challenging questions as you walk through the tutorial. You need to understand each step!


Example 1: Simplify: simplify expressions example 1.

Solution:
We first convert to a common denominator using the LCD (least common denominator) of 3 and 2 which is 6.

solution to example 1



Example 2: Simplify: simplify expressions example 2.

Solution:

We simplify by converting to the same denominator using the LCD of (x - 2) and (x + 1) which is is (x - 2)(x + 1) and applying the rule of the sum of two rational expressions.

solution to example 2



Example 3: Simplify: simplify expressions example 3.

Solution:

We simplify by converting to the same denominator

solution to example 3



Example 4: Simplify: simplify expressions example 4

Solution:

Apply the rule of subtraction of rational expressions to expression 1 in example 4 and expression 2 in example 4

expression 1 in solution of example 4

then simplify.

expression 2 in solution of example 4

Apply the rule of division of rational expressions ( which becomes a multiplication by the reciprocal ) and factor

expression 3 in solution of example 4

and simplify

expression 4 in solution of example 4



Example 5: Simplify: simplify expressions example 5

Solution:

Apply the rule of multiplication to expression 1 in example 5 and the rule of subtraction to expression 2 in example 5.

expression 1 in solution of example 5

Apply the rule of division (multiply be the reciprocal):

expression 2 in solution of example 5

Simplify.

expression 3 in solution of example 5



More Questions: Simplify the following expressions - Answers at the bottom of the page.

questions to simplify expressions

Answers to the above questions

solutions to above questions

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Updated: 20 January 2017 (A Dendane)