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# Find all values of x such that \frac{2x}{x + 2} = -\frac{6}{x + 4}. If you find more than one value,

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Find all values of x such that               $$\frac{2x}{x + 2} = -\frac{6}{x + 4}.$$
If you find more than one value, then list your solutions, separated by commas.

May 5, 2020
edited by mathlete2008  May 5, 2020

#1
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2x/(x + 2) = -6/(x + 4)

==> 2x(x + 2) = -6(x + 2)

==> 2x^2 + 2x = -6x - 12

==> 2x^2 + 8x - 12 = 0

==> x = sqrt(10) - 2, -sqrt(10) - 2 (quadratic formula)

May 5, 2020
#2
+87
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It said it was wrong.

May 5, 2020
#3
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What's "it"?

No offense, but I'm sure melody would agree, since i've seen her say it before.

I know how to use latex, but it's rather unpleasant to read raw code, even if it's easy for you just to copy from a website and paste it onto here.

$$\frac{2x}{x + 2} = -\frac{6}{x + 4}.$$

see? That's much better.

I don't know where this problem came from but i'm pretty sure it's from AoPS or something.

May 5, 2020
#4
+87
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Yeah, sorry.

May 5, 2020
#5
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"It" being the answer "x = sqrt(10) - 2, -sqrt(10) - 2."

May 5, 2020
edited by mathlete2008  May 5, 2020
#6
+87
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I fixed the question.

May 5, 2020
#7
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Get rid of the fractions by rearrangement, and then, rearrange to isolate x.

Here

2x * (x+4) = 6 * (x+2)

See what you can do.

I refered to "it" as the first it

You said "it said it was wrong"

WHO said it was wrong?

Ask if you have any questions :)

May 6, 2020
#8
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Stop trying to cheat on your homework.

May 9, 2020