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)

Re: Simplifying Rational Expressions (Fractions)

Quote:

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:

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

Go ahead!

Re: Simplifying Rational Expressions (Fractions)

I got scooped!

Ok earboth. Just take credit for giving the correct answer. See if I care! (Crying)

-Dan

Re: Simplifying Rational Expressions (Fractions)

In my frustration I completely overlooked simplifying. Thank you for your help!