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

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Answer 1 · 2017-06-07T23:57:01

$x=-2,12$

The first step is cross multiple:

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

Distribute:

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

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

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

Simplify:

$x^2-10x+24$

Factor and set the factors equal to zero:

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

Solve and you get:

$x=-2,12$

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