# Dividing rational expressions

### Dividing rational expressions

#### Lessons

$\bullet$ multiplication rule: $x^a \cdot x^b=x^{a+b}$
$\bullet$ division rule: $\frac{x^a}{x^b}=x^{a-b}$
• Introduction
$\bullet$ Review: Dividing Monomials

• 1.
Simplifying Rational Expressions Involving Division
State the restrictions on the variables, then simplify.

$\large \frac{81x}{64y^2} \div \frac{27x^2}{32y}$

• 2.
Simplifying Rational Expressions Involving both Multiplication and Division
State the restrictions on the variables, then simplify.
a)
$\frac{72x^4y^2}{8x^5z^3} \times \frac{y^2}{x^3} \div \frac{15x^4y^4}{15z^4}$

b)
$\frac{15x^4y^4}{18x^2z^7} \times \frac{5z^3}{5x^3y} \div \frac{25x^2y}{50z^5}$

• 3.
Dividing Rational Expressions in Factored Form
State the non-permissible values for x, then simplify:

$\large \frac{(x+2)}{(x-5)(x+4)} \div \frac{3(x+2)}{(x+4)(x)}$

• 4.
Convert Expressions to Factored Form, then Divide
State the non-permissible values for x, then simplify:

$\large \frac{3x^2-12x}{x^2-4} \div \frac{2x^3-8x^2}{x^2-x-6}$

• 5.
Fractions Dividing Fractions
State the non-permissible values for x, then simplify:

$\large \frac{ \frac{25x+10}{4x-10}}{\frac{25x^2+10x}{(2x-5)^2}}$

• 6.
$\large \frac{\frac{3}{2a+6}+\frac{4}{4a-4}}{\frac{3}{a}+5}$