# How can you evaluate (4a-2)/(3a+12) - (a-2)/(a+4) ?

Aug 3, 2015

$\frac{4 a - 2}{3 a + 12} - \frac{a - 2}{a + 4} = \frac{1}{3}$

#### Explanation:

In order to calculate the difference between the two terms, you need to write them with the same denominator. Notice that:

$3 a + 12 = 3 \cdot \left(a + 4\right)$

Therefore:

$\frac{a - 2}{a + 4} = 1 \cdot \frac{a - 2}{a + 4} = \frac{3}{3} \cdot \frac{a - 2}{a + 4} = \frac{3 \left(a - 2\right)}{3 \left(a + 4\right)} = \frac{3 a - 6}{3 a + 12}$

Therefore:

$\frac{4 a - 2}{3 a + 12} - \frac{a - 2}{a + 4} = \frac{4 a - 2}{3 a + 12} - \frac{3 a - 6}{3 a + 12}$

$= \frac{\left(4 a - 2\right) - \left(3 a - 6\right)}{3 a + 12}$

$= \frac{4 a - 2 - 3 a + 6}{3 a + 12} = \frac{4 a - 3 a + 6 - 2}{3 a + 12} = \frac{a + 4}{3 a + 12}$

$= \frac{a + 4}{3 \left(a + 4\right)} = \frac{1}{3}$