# How do you simplify a/(a+4)+6/(a+2)?

Oct 2, 2017

= $\frac{{a}^{2} + 8 a + 24}{{a}^{2} + 6 a + 8}$

#### Explanation:

$\frac{a}{a + 4} + \frac{6}{a + 2}$

Make the denominators equal to carry out addition of fractions:

=$\frac{a}{a + 4} \setminus \times \frac{a + 2}{a + 2} + \frac{6}{a + 2} \setminus \times \frac{a + 4}{a + 4}$

= $\frac{{a}^{2} + 2 a + 6 a + 24}{\left(a + 4\right) \left(a + 2\right)}$

= $\frac{{a}^{2} + 8 a + 24}{\left(a + 4\right) \left(a + 2\right)}$

= $\frac{{a}^{2} + 8 a + 24}{{a}^{2} + 6 a + 8}$