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This is for homework, and I could really use help on the last step. This is the original equation. I'm working on simplifying it. My math book is for Intermediate Algebra. $$ \dfrac{ 5x }{ x^2-25 } - \dfrac{5}{x+5} $$

I created the common denominator by multiplying both sides by their missing factor.

$$ \dfrac{ 5x^2+25x}{ (x^2-25)(x+5) } - \dfrac{5x^2-125}{(x^2-25)(x+5)} $$

I combined the terms, which gave me:

$$ \dfrac{ 25x+125 }{ (x^2-25)(x+5) } $$

I believe the answer is below, based on wolfram alpha.

I'm not sure how to simplify from here, to get the answer.

$$ \dfrac{25}{x^2-25} $$

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I'd have started by multiplying $x-5$ to the top and bottom of the second fraction... – J. M. Sep 14 '11 at 3:38

Notice that you can factor out a $25$ from the top of the fraction:

$\frac{25x + 125}{(x^2 - 25)(x + 5)}$ to obtain $\frac{25(x+5)}{(x^2 - 25)(x+5)}$

and I think you can finish after that :)

EDIT: The main lesson to take out of this is always look for common factors as they usually help simplify equations quite a bit

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