# How do you solve 12/(v^2-16) - 24/(v-4) = 3?

Mar 19, 2016

You have to put on an equal denominator.

#### Explanation:

First, factor the denominator to find the LCD (Least Common Denominator).

$\frac{12}{\left(v - 4\right) \left(v + 4\right)} - \frac{24}{v - 4} = 3$

The LCD is $\left(v - 4\right) \left(v + 4\right)$

$\frac{12}{\left(v - 4\right) \left(v + 4\right)} - \frac{24 \left(v + 4\right)}{\left(v - 4\right) \left(v + 4\right)} = \frac{3 \left(v - 4\right) \left(v + 4\right)}{\left(v - 4\right) \left(v + 4\right)}$

We can now eliminate the denominator since all the fractions are now equivalent.

$12 - 24 v + 96 = 3 \left({v}^{2} - 16\right)$

$12 - 24 v + 96 = 3 {v}^{2} - 48$

$0 = 3 {v}^{2} + 24 v - 156$

$0 = 3 \left({v}^{2} + 8 v - 52\right)$

Solving by completing the square since factoring isn't possible:

$0 + 52 = 1 \left({v}^{2} + 8 v + 16 - 16\right)$

$52 = {\left(v + 4\right)}^{2}$

$\pm \sqrt{52} = v + 4$

$\pm \sqrt{52} - 4 = v$

$\pm 2 \sqrt{13} - 4 = v$

Hopefully this helps!