How do you solve \frac { x } { x - 3} = \frac { 8} { x - 2}?

Jun 7, 2017

$x = - 2 , 12$

Explanation:

The first step is cross multiple:

$x \left(x - 2\right) = 8 \left(x - 3\right)$

Distribute:

${x}^{2} - 2 x = 8 x - 24$

Then subtract $- 8 x$ from both side and add $24$ to both sides.

${x}^{2} - 2 x - 8 x + 24 = 0$

Simplify:

${x}^{2} - 10 x + 24$

Factor and set the factors equal to zero:

$\left(x - 12\right) \left(x - 2\right) = 0$

Solve and you get:

$x = - 2 , 12$