SOLUTION: I can not figure out these problems! I have been having such a hard time. 6/x+2-6=x+3/x-2

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Question 587996: I can not figure out these problems! I have been having such a hard time.
6/x+2-6=x+3/x-2
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
6/x+2-6=x+3/x-2
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I think you mean
6%2F%28x%2B2%29-6=+%28x%2B3%29%2F%28x-2%29
Multiply by (x+2)
6+-+6%28x%2B2%29+=+%28x%2B3%29%2A%28x%2B2%29%2F%28x-2%29
Multiply by (x-2)
6%28x-2%29+-+6%28x%2B2%29%2A%28x-2%29+=+%28x%2B3%29%2A%28x%2B2%29
6x-12+-+6%28x%5E2-4%29+=+x%5E2+%2B+5x+%2B+6
6x-12+-+6x%5E2%2B24+=+x%5E2+%2B+5x+%2B+6
6x%2B12+-+6x%5E2+=+x%5E2+%2B+5x+%2B+6
6x%2B12+=+7x%5E2+%2B+5x+%2B+6
6x+=+7x%5E2+%2B+5x+-+6
0+=+7x%5E2+-+x+-+6
7x%5E2+-+x+-+6+=+0
(7x + 6)*(x - 1) = 0
x = 1
x = -6/7