Simplifying complex fractions

Lessons

• Introduction
  Introduction to Simplifying Complex Fractions
  a)

  Type 1: $\frac{single\;fraction}{single\;fraction}$
  
  
  b)

  Type 2: $\frac{multiple\;fraction}{multiple\;fraction}$
  
  
  c)

  Type 2 Special Case: Fractions Involving Negative Exponents
  
  

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

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

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• 3.
  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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