# How do you solve \frac { 8} { x - 5} = \frac { 6} { x + 9}?

May 15, 2017

Cross multiplication, then solve.
Answer: $x = - 51$

#### Explanation:

Solve $\frac{8}{x - 5} = \frac{6}{x + 9}$

First, we can cross multiply to get the variables out of the denominators:
$8 \left(x + 9\right) = 6 \left(x - 5\right)$

We can use the distributive property:
$8 x + 72 = 6 x - 30$

Now, we subtract $6 x$ from both sides and subtract $72$ from both sides and simplify:
$8 x + 72 - 6 x - 72 = 6 x - 30 - 6 x - 72$
$2 x = - 102$

Finally, we divide both sides by $2$ to isolate the $x$:
$x = - 51$