SOLUTION: These are rational equations. I need to solve. (3/x-2) + 1/2 = (x/x-2) Thanks!

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Question 768626: These are rational equations. I need to solve.
(3/x-2) + 1/2 = (x/x-2)
Thanks!
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Not sure if you mean what you wrote, %283%2Fx-2%29+%2B+1%2F2+=+%28x%2Fx-2%29, or something else like maybe 3%2F%28x-2%29%2B1%2F2=x%2F%28x-2%29.
(EDIT: SEE MUCH LOWER DOWN, THE EQUATION YOU REALLY WANTED HELP WITH.)

Using exactly what you wrote, %283%2Fx-2%29+%2B+1%2F2+=+%28x%2Fx-2%29, multiply both members by x.
3-2x%2Bx%2F2=x-2x
3%2Bx%2F2=x
3=x-x%2F2
3=x%2F2
x=6


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THIS IS THE EQUATION YOU REALLY WANTED TO SHOW:
3%2F%28x-2%29%2B1%2F2=x%2F%28x-2%29
The simplest common denominator is 2*(x-2), so multiply both members by this product.

+2%28x-2%29%283%2F%28x-2%29%29%2B%282%28x-2%29%29%281%2F2%29=2%28x-2%29%28x%2F%28x-2%29%29
You can find what factors between numerators and denominators cancel,...
2%2A3%2Bx-2=2x
6-2=x
FINAL ANSWER: highlight%28x=4%29