2
$\begingroup$

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} $

  • 0
    I'd have started by multiplying $x-5$ to the top and bottom of the second fraction...2011-09-14

1 Answers 1

4

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