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*}