#### Answer

$x = 7$

#### Work Step by Step

$\frac{8}{x + 9} = \frac{2}{x - 3}$
The cross products property states that the product of the means is the product of the extremes. Get rid of the fractions by using the cross products property to multiply the numerator of one fraction with the denominator of the other fraction, and vice versa:
$8(x - 3) = 2(x + 9)$
Use the distributive property first:
$8x - 24 = 2x + 18$
Subtract $2x$ from each side of the equation to move variables to the left side of the equation:
$6x - 24 = 18$
Add $24$ to each side of the equation to move constants to the right side of the equation:
$6x = 42$
Divide each side by $6$ to solve for $x$:
$x = 7$