SOLUTION: 2/3=2-5x-3/x-1 Does the x-1 make this an undefined operation? Or is it solvable?

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Question 150906: 2/3=2-5x-3/x-1
Does the x-1 make this an undefined operation? Or is it solvable?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%282%29%2F%283%29=2-%285x-3%29%2F%28x-1%29 Start with the given equation.


Multiply every term on both sides by the LCD 3%28x-1%29. Doing this will eliminate all of the fractions.



2%28x-1%29=6%28x-1%29-3%285x-3%29 Simplify.


2x-2=6x-6-15x%2B9 Distribute.


2x-2=-9x%2B3 Combine like terms on the right side.


2x=-9x%2B3%2B2 Add 2 to both sides.


2x%2B9x=3%2B2 Add 9x to both sides.


11x=3%2B2 Combine like terms on the left side.


11x=5 Combine like terms on the right side.


x=%285%29%2F%2811%29 Divide both sides by 11 to isolate x.


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Answer:

So the answer is x=5%2F11


Which approximates to x=0.455


Note: if you plug in x=5%2F11 back into the equation, you will get a real number (ie you won't get a division by zero). So this means that x=5%2F11
is a solution.