# Divide Rational Expressions

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

## Examplex/(3x - 1) ÷ (x + 7)/2x

Solution

Solution (Detail)

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 = 2x^{2}

(3x - 1)⋅(x + 7) = (3x - 1)(x + 7)

So

2x^{2}/(3x - 1)(x + 7)

is the answer.

## Example(x^{2} - 4)/(x - 1) ÷ (x + 2)/5

Solution

Solution (Detail)

Factor the numerator

x^{2} - 4.

x^{2} - 4

= (x + 2)(x - 2)

Factor the Difference of Two Squares: a^{2} - b^{2}

x^{2} - 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.