How do you add or subtract (x+6)/(5x+10) - (x-2)/(4x+8)?

May 25, 2015

Notice that the denominator of each of these terms is a simple multiple of $\left(x + 2\right)$, so we only need to multiply by constants to make the denominators of the two terms the same:

$\frac{x + 6}{5 x + 10} - \frac{x - 2}{4 x + 8}$

$= \frac{x + 6}{5 \left(x + 2\right)} - \frac{x - 2}{4 \left(x + 2\right)}$

$= \frac{4 \cdot \left(x + 6\right)}{4 \cdot 5 \left(x + 2\right)} - \frac{5 \cdot \left(x - 2\right)}{5 \cdot 4 \left(x + 2\right)}$

$= \frac{4 \left(x + 6\right)}{20 \left(x + 2\right)} - \frac{5 \left(x - 2\right)}{20 \left(x + 2\right)}$

$= \frac{4 \left(x + 6\right) - 5 \left(x - 2\right)}{20 \left(x + 2\right)}$

$= \frac{4 x + 24 - 5 x + 10}{20 \left(x + 2\right)}$

$= \frac{14 - x}{20 \left(x + 2\right)}$

$= \frac{14 - x}{20 x + 40}$