# Dividing rational expressions

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##### Intros
###### Lessons
1. $\bullet$ Review: Dividing Monomials
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##### Examples
###### Lessons
1. Simplifying Rational Expressions Involving Division
State the restrictions on the variables, then simplify.

$\large \frac{81x}{64y^2} \div \frac{27x^2}{32y}$
1. Simplifying Rational Expressions Involving both Multiplication and Division
State the restrictions on the variables, then simplify.
1. $\frac{72x^4y^2}{8x^5z^3} \times \frac{y^2}{x^3} \div \frac{15x^4y^4}{15z^4}$
2. $\frac{15x^4y^4}{18x^2z^7} \times \frac{5z^3}{5x^3y} \div \frac{25x^2y}{50z^5}$
2. Dividing Rational Expressions in Factored Form
State the non-permissible values for x, then simplify:

$\large \frac{(x+2)}{(x-5)(x+4)} \div \frac{3(x+2)}{(x+4)(x)}$
1. Convert Expressions to Factored Form, then Divide
State the non-permissible values for x, then simplify:

$\large \frac{3x^2-12x}{x^2-4} \div \frac{2x^3-8x^2}{x^2-x-6}$
1. Fractions Dividing Fractions
State the non-permissible values for x, then simplify:

$\large \frac{ \frac{25x+10}{4x-10}}{\frac{25x^2+10x}{(2x-5)^2}}$
1. Performing Addition First, then Division
Simplify:

$\large \frac{\frac{3}{2a+6}+\frac{4}{4a-4}}{\frac{3}{a}+5}$
###### Topic Notes
$\bullet$ multiplication rule: $x^a \cdot x^b=x^{a+b}$
$\bullet$ division rule: $\frac{x^a}{x^b}=x^{a-b}$