Divide Rational Expressions

How to divide rational expressions: 2 examples and their solutions.

Example 1

Example

Solution

To solve the division sign [ ÷ ],

change [ ÷ ] to [ ⋅ ],

and switch the numerator and the denominator
of the fraction right behind [ ÷ ]:
(x + 7)/2x → 2x/(x + 7).

x⋅2x = 2x2

(3x - 1)⋅(x + 7) = (3x - 1)(x + 7)

So 2x2/(3x - 1)(x + 7) is the answer.

Example 2

Example

Solution

Factor the numerator
x2 - 4.

x2 - 4
= (x + 2)(x - 2)

Factor the Difference of Two Squares: a2 - b2

x2 - 4
= (x + 2)(x - 2)

So (given) = (x + 2)(x - 2)/(x - 1) ÷ (x + 2)/5.

Change [ ÷ ] to [ ⋅ ],

and switch the numerator and the denominator
of the fraction right behind [ ÷ ]:
(x + 2)/5 → 5/(x + 2).

Cancel the common factor (x + 2).

Then 5(x - 2)/(x - 1).

Simplify a Rational Expression

So 5(x - 2)/(x - 1) is the answer.