SOLUTION: x-3/4-2x - 1/x-2 + 1 = 0

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Question 151208: x-3/4-2x - 1/x-2 + 1 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-3%29%2F%284-2x%29+-+1%2F%28x-2%29+%2B+1+=+0 Start with the given equation.


%28x-3%29%2F%28-2%28x-2%29%29+-+1%2F%28x-2%29+%2B+1+=+0 Factor 4-2x to get 4-2x=2%282-x%29=-2%28x-2%29


%28-%28x-3%29%29%2F%282%28x-2%29%29+-+1%2F%28x-2%29+%2B+1+=+0 Simplify


%28-x%2B3%29%2F%282%28x-2%29%29+-+1%2F%28x-2%29+%2B+1+=+0 Distribute the negative.



Multiply every term on both sides by the LCD 2%28x-2%29. Doing this will eliminate all of the fractions.


-x%2B3%2B2%28-1%29%2B2%28x-2%29=0 Multiply and simplify.


-x%2B3-2%2B2x-4=0 Distribute.


x-3=0 Combine like terms on the left side.


x=0%2B3 Add 3 to both sides.


x=3 Combine like terms on the right side.


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Answer:

So the answer is x=3