SOLUTION: 1/(x-4) - 5/(x+2)=6/(x^2-2x-8)

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Question 67337: 1/(x-4) - 5/(x+2)=6/(x^2-2x-8)
Found 2 solutions by Earlsdon, stanbon:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F%28x-4%29+-+5%2F%28x%2B2%29+=+6%2F%28x%5E2-2x-8%29 Simplify the left side.
%28%28x%2B2%29-5%28x-4%29%29%2F%28x%5E2-2x-8%29+=+6%2F%28x%5E2-2x-8%29 Multiply both sides by x%5E2-2x-8
%28x%2B2%29-5%28x-4%29+=+6 Simplify the left side.
x%2B2-5x%2B20+=+6
-4x%2B22+=+6 Subtract 22 from both sides.
-4x+=+-16 Divide both sides by -4
x+=+4
But! x=4 is an excluded value because it would make the denominator of the first term othe equation undefined: 1%2F%284-4%29+=+1%2F0 and this is undefined.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
1/(x-4) - 5/(x+2)=6/(x^2-2x-8)
The least common multiple is (x-4)(x+2)=x^2-2x-8
Multiply thru by the lcm to get:
(x+2) - 5(x-4) = 6
x-2-5x+20 = 6
x^2-5x+14=0
(x-7)(x+2)=0
x=7 or x=-2
Comment: x cannot be -2 as that would cause a zero in the denominator
or the original problem
So, x=7 is the only solution.
cheers,
Stan H>