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How would I go about simplifying this fraction:

$$\frac{\frac{1}{x} - \frac{1}{a}}{x - a}$$

I've looked at similar questions such as this one but still can't seem to figure this one out. Any help would be greatly appreciated!

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    $\begingroup$ Hint: the number $1$ can be written many different ways and any expression multiplied by $1$ does not change the value of the expression. $\endgroup$ – Kevin Driscoll Sep 13 '13 at 2:03
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$$ \frac{\frac{1}{x}-\frac{1}{a}}{x-a}=\frac{\frac{a-x}{ax}}{x-a}=\frac{a-x}{ax} \cdot \frac{1}{x-a}=\frac{-1}{xa} $$

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Expanding $$\frac{\frac{1}{x}-\frac{1}{a}}{x-a}$$ by $a\cdot x$ yields $$\frac{a-x}{ax(x-a)}=-\frac{1}{ax}.$$

Michael

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