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

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) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Multiply every term on both sides by the LCD . Doing this will eliminate all of the fractions.

Simplify.

Distribute.

Combine like terms on the right side.

Add to both sides.

Add to both sides.

Combine like terms on the left side.

Combine like terms on the right side.

Divide both sides by to isolate .

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Answer:

So the answer is

Which approximates to

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