# Thread: Simplifying Rational Expressions (Fractions)

1. ## Simplifying Rational Expressions (Fractions)

I am having trouble with the following problem.

1/x - 1/5
1/x^2 - 1/25

I know the answer ends up being:
5x
x+5

How do I do the work to find this answer? Thanks!

(Also I do know how to simplify expressions like this, it's just that the fractions are killing me)

2. ## Re: Simplifying Rational Expressions (Fractions)

Originally Posted by Diesal
I am having trouble with the following problem.

1/x - 1/5
1/x^2 - 1/25

I know the answer ends up being:
5x
x+5

How do I do the work to find this answer? Thanks!

(Also I do know how to simplify expressions like this, it's just that the fractions are killing me)
I assume that you mean:

$\displaystyle \frac{\frac1x - \frac15}{\frac1{x^2} - \frac1{25}} = \frac{\frac1x - \frac15}{\left( \frac1x - \frac15 \right) \left( \frac1x + \frac15 \right)}$

Cancel the common term:

$\displaystyle \frac1{\frac1x + \frac15} = \frac1{\frac5{5x} + \frac x{5x}} = \frac1{\frac{5+x}{5x}}$