SOLUTION: 16 / (x+2) = 1 + 2/(x-4) I first eliminated the denominator x+2, then the denominator x-4. Simplifying and setting equal to 0, I get x = -6, -10. These solutions do not work,

Question 790553: 16 / (x+2) = 1 + 2/(x-4)
I first eliminated the denominator x+2, then the denominator x-4. Simplifying and setting equal to 0, I get x = -6, -10. These solutions do not work, but their positives do. I don't understand how to solve this equation without getting negative values for x.
Thanks in advance.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
I get 6 and 10.
You must have made some small mistake.
It is very hard to notice one's own mistakes.

Multiplying both sides times I get

which simplifies to

Factoring, I get

So, either --> ,
or --> .

If you do not like factoring, you could use the quadratic formula, or "complete the square" instead.

Completing the square:

So either --> --> ,
or --> -->

Using the quadratic formula:
The solutions to are given by .
In the case of ,
, , and , so
.
The solutions are

and

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