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Rational expressions

Getting a common denominator of algebraic fractions

  • If you need to add or subtract two rational expressions, work with them in the same way as adding and subtracting normal fractions.
  • Firstly find the lowest common denominator (LCD) and make each fraction an equivalent fraction.
  • Expand any brackets.
    For example:
    \begin{eqnarray*}
    \frac{x}{x-3} + \frac{5}{x+2}
    &=& \frac{x(x+2)+5(x-3)}{(x-3)(x+2)} \\
    &=& \frac{x^2+ 2x+5x-15}{x^2 + 2x-3x-6} \\
    &=& \frac{x^2 + 7 x - 15}{x^2 - x - 6} 
    \end{eqnarray*}