How do you simplify (a+2)/(a-4) + (a-2)/(a+3)?

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