# Simplifying Rational Expressions HELP

• Mar 16th 2013, 08:14 AM
alegbro
Simplifying Rational Expressions HELP
Hi all,

I cannot understand why this does not work.

$\displaystyle \frac{x^{2} + 6x + 5}{x^{2} -x -2}$

So I thought I could just cancel out the fraction x^2 in both the numerator and dominator as it is a common factor.
Why does this not work?

For example, the fraction below we can simplify it by dividing top and bottom by 5 and p^2 as they are common factors.

$\displaystyle \frac{60p^{3}q}{35p^{5}r} = \frac{12q}{7p^{2}r}$

So why does the above one not let us divide by x^2 as it is also a common factor?
• Mar 16th 2013, 08:28 AM
princeps
Re: Simplifying Rational Expressions HELP
Hint :

$\displaystyle x^2+6x+5=(x+1)(x+5)$
• Mar 16th 2013, 08:57 AM
alegbro
Re: Simplifying Rational Expressions HELP
That doesn't explain anything to me :S

I know what a quadradric is but I still don't get why we can't factor out the top and bottom by x^2.
• Mar 16th 2013, 09:26 AM
HallsofIvy
Re: Simplifying Rational Expressions HELP
The problem is that you have an incorrect idea of what a factor is! $\displaystyle x^2$ is NOT a factor in both numerator and denominator because it is added, not multiplied. "Factors" are parts of products, not sums.
• Mar 16th 2013, 09:28 AM
princeps
Re: Simplifying Rational Expressions HELP
$\displaystyle \frac{4+5}{4+2}\neq \frac{5}{2}$