Dividing Rational Expressions

How to divide rational expressions?
A rational expression is a fraction in which either the numerator, or the denominator, or both the numerator and the denominator are algebraic expressions.

To divide a fraction by another fraction, we multiply the first fraction by the reciprocal of the second fraction. In other words, when you change the operation from ÷ to ×, you need to change the second fraction to its reciprocal by reversing the numerator and the denominator. Similarly, when we divide rational expressions, we “flip” the second expression and then we multiply the two expressions.

The following diagram shows how to divide rational expressions. Scroll down the page for more examples and solutions.

 

Example:

Simplify the following expressions:

Solution:

How to divide rational expressions?

How to divide rational expressions containing trinomials?

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