# How do you combine 4/(a^2 + 12a +27) + 5/(a^2 +10a +21)?

Jun 2, 2015

Since ${a}^{2} + 12 a + 27 = \left(a + 3\right) \left(a + 9\right)$
and ${a}^{2} + 10 a + 21 = \left(a + 3\right) \left(a + 7\right)$

The Least Common Divisor needed to combine these two terms is
$\left(a + 3\right) \left(a + 7\right) \left(a + 9\right)$

$\frac{4}{{a}^{2} + 12 a + 27} + \frac{5}{{a}^{2} + 10 a + 21}$

$= \frac{4 \left(a + 7\right) + 5 \left(a + 9\right)}{\left(a + 3\right) \left(a + 7\right) \left(a + 9\right)}$

$= \frac{9 a + 73}{\left(a + 3\right) \left(a + 7\right) \left(a + 9\right)}$