# Simplifying complex fractions

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### Introduction

#### Lessons

1. Introduction to Simplifying Complex Fractions
2. Type 1: $\frac{single\;fraction}{single\;fraction}$
3. Type 2: $\frac{multiple\;fraction}{multiple\;fraction}$
4. Type 2 Special Case: Fractions Involving Negative Exponents
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### Examples

#### Lessons

1. Type 1: $\frac{single\;fraction}{single\;fraction}$
simplify:
i) $\frac{\frac{2}{3}}{\frac{8}{9}}$
ii) $\frac{\frac{12x^5y^3}{3x^2}}{\frac{2xy^7}{y^2}}$
iii) $\frac{\frac{5x-10}{5}}{\frac{x-2}{x}}$
1. Type 2: $\frac{multiple\;fraction}{multiple\;fraction}$
simplify:
i) $\frac{\frac{x^2}{y^3}-\frac{1}{y}}{\frac{y^2}{x^3}-\frac{1}{x}}$
ii) $\frac{1-\frac{4}{z}+\frac{4}{z^2}}{\frac{1}{z^2}-\frac{2}{z^3}}$
1. Fractions Involving Negative Exponents
Simplify:
i) $\frac{x^{-1}-3x^{-2}}{3x^{-1}-9x^{-2}}$
ii) $(x^{-2}-y^{-2})^{-1}$

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###### Topic Basics
Steps to solving complex fractions:
1. Write the main numerator and denominator as single fractions.
2. Set up a division statement.
3. Simplify the expression.