SOLUTION: Solve the rational equation: x(2x+1)/x-2= 10/x-2-5/2

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Question 671445: Solve the rational equation:

x(2x+1)/x-2= 10/x-2-5/2
Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
Is this
%28x%282x%2B1%29%29%2F%28x-2%29+=+10%2F%28x-2%29+-+5%2F2
...
If so,
%282x%5E2%2Bx%29%2F%28x-2%29+=+10%2F%28x-2%29+-+5%2F2
...
Multiply the entire equation by 2(x-2)
2%282x%5E2+%2B+x%29+=+20+-+5%28x-2%29
4x%5E2+%2B+2x+=+20+-+5x+%2B+10
...
Combine like terms
4x%5E2+%2B+2x+%2B+5x+=+20+%2B+10
highlight_green%284x%5E2+%2B+7x+-30+=+0%29
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