SOLUTION: 3x/x-1 + 6x-9/x-1 -6 =0 solve for x. the numbers in front are fractions

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Question 150778: 3x/x-1 + 6x-9/x-1 -6 =0 solve for x. the numbers in front are fractions
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%283x%29%2F%28x-1%29%2B%286x-9%29%2F%28x-1%29-6=0 Start with the given equation.


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


3x%2B6x-9-6%28x-1%29=0 Simplify.



3x%2B6x-9-6x%2B6=0 Distribute.


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


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


3x=3 Combine like terms on the right side.


x=%283%29%2F%283%29 Divide both sides by 3 to isolate x.


x=1 Reduce.



So x=1 is a possible solution. However, we must check it.



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Check:

Let's test the possible solution x=1:



%283x%29%2F%28x-1%29%2B%286x-9%29%2F%28x-1%29-6=0 Start with the given equation


%283%281%29%29%2F%281-1%29%2B%286%281%29-9%29%2F%281-1%29-6=0 Plug in x=1.


%283%29%2F%281-1%29%2B%286-9%29%2F%281-1%29-6=0 Multiply


%283%29%2F%280%29%2B%28-3%29%2F%280%29-6=0 Subtract. Since division by zero is undefined, this means that x=1 is not a solution.


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Answer:

So there are no solutions.