anonymous
  • anonymous
(x)/(x-2) - (-2)/(x+2)=(8)/(4-x^2)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Hero
  • Hero
\[\frac{x}{x - 2} - \frac{-2}{x + 2} = \frac{8}{4 - x^2}\] For convenience express the middle fraction as an addition: \[\frac{x}{x - 2} + \frac{2}{x + 2} = \frac{8}{4 - x^2}\] And make sure the denominators are factored: \[\frac{x}{x - 2} + \frac{2}{x + 2} = \frac{8}{(2 + x)(2 - x)}\]
anonymous
  • anonymous
I know this but how do i reverse the (2-x) ?
Hero
  • Hero
Okay to reverse that, take out a negative like so: \[\frac{x}{x - 2} + \frac{2}{x + 2} = -\frac{8}{(x+2)(x-2)}\]

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anonymous
  • anonymous
Then I add this on both sides.
Hero
  • Hero
Here's what to do...
Hero
  • Hero
Add the fraction on the right to both sides; subtract 2/(x + 2) from both sides: \[\frac{x}{x - 2} +\frac{8}{(x+2)(x-2)}= -\frac{2}{x + 2} \]
anonymous
  • anonymous
Why ?
Hero
  • Hero
Actually...
Hero
  • Hero
Instead of doing that...
Hero
  • Hero
Lets reduce x/(x - 2)
Hero
  • Hero
It's too bad you found out that way. It is better to discover such things on your own.
Hero
  • Hero
I'm going to continue posting my solution anyway.
anonymous
  • anonymous
Thank you.
Hero
  • Hero
You should try to figure it out on your own why no solutions exist.
anonymous
  • anonymous
The result is \[\frac{ x+2 }{ x-2 }\]
anonymous
  • anonymous
I think.
anonymous
  • anonymous
*=0

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