<s>[INST] Simplifying $(1/x-1/5 )/( 1/x^2-1/25)$ How do I get $\frac{5x}{x+5}$ from simplifying the following? 
$$\frac{(\frac{1}{x}-\frac{1}{5} )}{( \frac{1}{x^2}-\frac{1}{25})}$$
My work:
I multiplied the top and bottom by the LCD: $25x^2$ (to get the same denominators).
Then I got: $\frac{25x-5x}{25-x^2}$ 
Then I got this for my answer: $\frac{20}{-(x-5)(x+5)}$
But the real answer is: $\frac{5x}{x+5}$
So my questions is how to I get from $\frac{20}{-(x-5)(x+5)}$ to $\frac{5x}{x+5}$?
 [/INST] $$\frac{\frac1x-\frac15}{\frac1{x^2}-\frac1{25}}=\frac{\frac{5-x}{5x}}{\frac{25-x^2}{25x^2}}$$
$$=\frac{25x^2(5-x)}{5x(25-x^2)}=\frac{5x}{5+x}$$ assuming $x(5-x)\ne0$
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