SOLUTION: Solve: 3/x-1=6/x+2

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Question 94433: Solve:
3/x-1=6/x+2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3%2F%28x-1%29=6%2F%28x%2B2%29 Start with the given equation

%28x-1%29%28x%2B2%29%283%2F%28x-1%29%29=%28x-1%29%28x%2B2%29%286%2F%28x%2B2%29%29 Multiply both sides by the LCD %28x-1%29%28x%2B2%29

Cancel like terms

3%28x%2B2%29=6%28x-1%29 Simplify

3x%2B6=6x-6 Distribute



3x%2B6-6x=-6 Subtract 6x from both sides


3x-6x=-6-6Subtract 6 from both sides


-3x=-6-6 Combine like terms on the left side


-3x=-12 Combine like terms on the right side


x=%28-12%29%2F%28-3%29 Divide both sides by -3 to isolate x



x=4 Reduce

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Answer:
So our answer is x=4



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Check:


3%2F%28x-1%29=6%2F%28x%2B2%29 Start with the given equation

3%2F%284-1%29=6%2F%284%2B2%29 Plug in x=4


3%2F3=6%2F6 Simplify the denominator


1=1 Reduce. Since the two sides of the equation are equal, this verifies our answer.