# Simplifying complex fractions

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### Introduction

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### Examples

#### Lessons

- 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) $\frac{\frac{5x-10}{5}}{\frac{x-2}{x}}$

- 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) $\frac{1-\frac{4}{z}+\frac{4}{z^2}}{\frac{1}{z^2}-\frac{2}{z^3}}$

- Fractions Involving Negative Exponents

Simplify:

i) $\frac{x^{-1}-3x^{-2}}{3x^{-1}-9x^{-2}}$

ii) $(x^{-2}-y^{-2})^{-1}$