$\bullet$ division rule: $\frac{x^a}{x^b}=x^{a-b}$

# Dividing Rational Expressions: Mastering Advanced Algebra Unlock the secrets of dividing rational expressions with our comprehensive guide. Learn essential techniques, avoid common pitfalls, and boost your algebra skills through step-by-step instructions and practice problems.

Examples

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**Simplifying Rational Expressions Involving Division**

State the restrictions on the variables, then simplify.

$\large \frac{81x}{64y^2} \div \frac{27x^2}{32y}$**Simplifying Rational Expressions Involving both Multiplication and Division**

State the restrictions on the variables, then simplify.**Dividing Rational Expressions in Factored Form**

State the non-permissible values for x, then simplify:

$\large \frac{(x+2)}{(x-5)(x+4)} \div \frac{3(x+2)}{(x+4)(x)}$**Convert Expressions to Factored Form, then Divide**

State the non-permissible values for x, then simplify:

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

State the non-permissible values for x, then simplify:

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

Simplify:

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