# How do you combine (2a + 1)/(3a+2) - (a-4)/(2-3a)?

##### 1 Answer
May 20, 2015

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

cross multiplying for a common denominator :
$\frac{\left(2 a + 1\right) \times \left(2 - 3 a\right) - \left(a - 4\right) \times \left(3 a + 2\right)}{\left(3 a + 2\right) \left(2 - 3 a\right)}$

$\frac{4 a - 6 {a}^{2} + 2 - 3 a - \left(3 {a}^{2} + 2 a - 12 a - 8\right)}{\left(\cancel{6} a - 9 {a}^{2} + 4 - \cancel{6} a\right)}$

$= \frac{- 6 {a}^{2} - 3 {a}^{2} + 4 a - 3 a - 2 a + 12 a + 2 + 8}{- 9 {a}^{2} + 4}$
$= \frac{- 9 {a}^{2} + 11 a + 10}{- 9 {a}^{2} + 4}$

$= \frac{9 {a}^{2} - 11 a - 10}{9 {a}^{2} - 4}$