# How do you solve rational equations 4/(t+2)= - 4/(3t+6) + 8?

Apr 2, 2018

$t = - \frac{4}{3}$

#### Explanation:

Multiply both sides by $\left(t + 2\right) \left(3 t + 6\right)$ to get rid of the fractions

$4 \left(3 t + 6\right) = - 4 \left(t + 2\right) + 8 \left(t + 2\right) \left(3 t + 6\right)$

$12 t + 24 = - 4 t - 8 + 8 \left(3 {t}^{2} + 12 t + 12\right)$

$12 t + 24 = - 4 t - 8 + 24 {t}^{2} + 96 t + 96$

$24 {t}^{2} + 80 t + 64 = 0$

$3 {t}^{2} + 10 t + 8 = 0$

$\left(3 t + 4\right) \left(t + 2\right) = 0$

$t = - 2 \mathmr{and} - \frac{4}{3}$

If you substitute these values into the original question then the answer is $t = - \frac{4}{3}$