# How do you solve (a-2)/(a+3)-1=3/(a+2) and check for extraneous solutions?

Sep 4, 2016

$a = - \frac{19}{8}$

#### Explanation:

Put on a common denominator.

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

Eliminate the denominators and solve the resulting quadratic.

${a}^{2} - 4 - 1 \left({a}^{2} + 5 a + 6\right) = 3 a + 9$

${a}^{2} - 4 - {a}^{2} - 5 a - 6 = 3 a + 9$

$- 8 a = 19$

$a = - \frac{19}{8}$

Hopefully this helps!