What is the solution to the proportion $(x+10)/(x-6) = x/(x+4)$ ?

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Answer 1 · 2015-05-12T02:17:08

When solving a proportion problem (like this problem), one approach is to "cross multiply".

The idea is that fraction $a/b$ is equal to $m/n$ exactly when $an$ bm#.

So, to solve

$(x+10)/(x-6) = x/(x+4)$

We cross multiply, to get:

$(x+10)(x+4) =x (x-6)$

So, $x^2+4x+10x+40 = x^2-6x$

$x^2+14x+40=x^2-6x$

Sutracting $x^2$ from both sides gets us

$14x+40=-6x$ . Adding $6x$ and subtracting $40$ on both sides yields:

$20x=-40$ , so $x=-2$

We are not quite finished. Because we multiplied by expressions involving a variable, we need to.make sure we did not multiply by $0$ .

When $x=-2$ , neither $x-6$ nor $x+4$ is zero, so we should be ok.

As a final check make sure that

$((-2)+10)/((-2)-6)$ is equal to $(-2)/((-2)+4)$ .

What is the solution to the proportion (x+10)/(x-6) = x/(x+4)(x+10)/(x-6) = x/(x+4)?