SOLUTION: Evaluate the limit, if it exisit lim goes to 3 of 1/x-1/3/x-3

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Question 986716: Evaluate the limit, if it exisit lim goes to 3 of 1/x-1/3/x-3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, let's simplify the given expression


%281%2Fx+-+1%2F3%29%2F%28x-3%29


%28red%283x%29%2A%281%2Fx+-+1%2F3%29%29%2F%28red%283x%29%2A%28x-3%29%29 Multiply top and bottom by the inner LCD 3x.


%28red%283x%29%2A%281%2Fx%29+-+red%283x%29%2A%281%2F3%29%29%2F%28red%283x%29%2A%28x-3%29%29 Distribute through the numerator


%283-x%29%2F%283x%2A%28x-3%29%29 Multiply. Notice how the upper fractions go away


%28-%28-3%2Bx%29%29%2F%283x%2A%28x-3%29%29 Factor out -1 from the numerator


%28-%28x-3%29%29%2F%283x%2A%28x-3%29%29 Rearrange terms


%28-1%2Across%28%28x-3%29%29%29%2F%283x%2Across%28%28x-3%29%29%29 Cancel the x-3 terms


%28-1%29%2F%283x%29


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Now plug in x = 3


%28-1%29%2F%283x%29


%28-1%29%2F%283%2A3%29 Replace every 'x' with 3


-1%2F9


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So





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