Question 986716
First, let's simplify the given expression



{{{(1/x - 1/3)/(x-3)}}}



{{{(red(3x)*(1/x - 1/3))/(red(3x)*(x-3))}}} Multiply top and bottom by the inner LCD 3x.



{{{(red(3x)*(1/x) - red(3x)*(1/3))/(red(3x)*(x-3))}}} Distribute through the numerator



{{{(3-x)/(3x*(x-3))}}} Multiply. Notice how the upper fractions go away



{{{(-(-3+x))/(3x*(x-3))}}} Factor out -1 from the numerator



{{{(-(x-3))/(3x*(x-3))}}} Rearrange terms



{{{(-1*cross((x-3)))/(3x*cross((x-3)))}}} Cancel the {{{x-3}}} terms



{{{(-1)/(3x)}}}



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Now plug in x = 3



{{{(-1)/(3x)}}}



{{{(-1)/(3*3)}}} Replace every 'x' with 3



{{{-1/9}}}



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So 



*[Tex \LARGE \lim_{x \to 3} \left( \frac{\frac{1}{x}-\frac{1}{3}}{x-3} \right) = -\frac{1}{9}]



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