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Adding and subtracting algebraic fractions

Addition and subtraction of algebraic fractions follows the same rules as numerical fractions. The fractions are converted so that they have the same denominator and the numerators are then added or subtracted.

  • Addition \begin{align*} \frac{1}{\Tred{a}}+\frac{2}{\Torange{a+1}} &= \frac{\Torange{(a+1)}}{\Tred{a}\Torange{(a+1)}} + \frac{2\Tred{a}}{\Tred{a}\Torange{(a+1)}}\\ &= \frac{\Torange{(a+1)} + 2\Tred{a}}{\Tred{a}\Torange{(a+1)}}\\ &= \frac{3a+1}{a^2+a} \end{align*}
  • Subtraction \begin{align*} \frac{\Tblue{2x+1}}{\Tred{x-1}}-\frac{\Tgreen{x-2}}{\Torange{x+1}} &= \frac{\Tblue{(2x+1)}\Torange{(x+1)}}{\Tred{(x-1)}\Torange{(x+1)}} - \frac{\Tred{(x-1)}\Tgreen{(x-2)}}{\Tred{(x-1)}\Torange{(x+1)}}\\ &= \frac{\Tblue{(2x+1)}\Torange{(x+1)}-\Tred{(x-1)}\Tgreen{(x-2)}}{\Tred{(x-1)}\Torange{(x+1)}}\\ &= \frac{(2x^2+3x+1)-(x^2-3x+2)}{x^2-1}\\ &= \frac{x^2+6x+3}{x^2-1} \end{align*}