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.

mathlete2008 May 5, 2020

#1**0 **

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)

Guest May 5, 2020

#3**+2 **

What's "it"?

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

"Please arrange your problem properly".

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.

hugomimihu May 5, 2020

#7**+3 **

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 :)

hugomimihu May 6, 2020