Simplifying complex fractions

Simplifying complex fractions

Lessons

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.
  • 1.
    Type 1: singlefractionsinglefraction\frac{single\;fraction}{single\;fraction}
    simplify:
    i) 2389\frac{\frac{2}{3}}{\frac{8}{9}}
    ii) 12x5y33x22xy7y2\frac{\frac{12x^5y^3}{3x^2}}{\frac{2xy^7}{y^2}}
    iii) 5x105x2x\frac{\frac{5x-10}{5}}{\frac{x-2}{x}}

  • 2.
    Type 2: multiplefractionmultiplefraction\frac{multiple\;fraction}{multiple\;fraction}
    simplify:
    i) x2y31yy2x31x\frac{\frac{x^2}{y^3}-\frac{1}{y}}{\frac{y^2}{x^3}-\frac{1}{x}}
    ii) 14z+4z21z22z3\frac{1-\frac{4}{z}+\frac{4}{z^2}}{\frac{1}{z^2}-\frac{2}{z^3}}

  • 3.
    Fractions Involving Negative Exponents
    Simplify:
    i) x13x23x19x2\frac{x^{-1}-3x^{-2}}{3x^{-1}-9x^{-2}}
    ii) (x2y2)1(x^{-2}-y^{-2})^{-1}