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

Question

1189 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-06-07T23:57:01

$x = - 2, 12$ $x=-2,12$

The first step is cross multiple:

$x (x - 2) = 8 (x - 3)$ $x(x-2)=8(x-3)$

Distribute:

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

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

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

Simplify:

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

Factor and set the factors equal to zero:

$(x - 12) (x - 2) = 0$ $(x-12)(x-2)=0$

Solve and you get:

$x = - 2, 12$ $x=-2,12$

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