# Thread: [SOLVED] rational polynomial common denominator

1. ## [SOLVED] rational polynomial common denominator

Hi,

I really don't want someone to work out the whole problem for me. Just a quick question Thanks!

$\frac{1}{x+3} + \frac{1}{x^2 + 5x +6}$

When I am getting a common denominator here, Should I factor the quadratic first or go ahead and multiply to get a common denominator? Or does it really make a difference?
thanks!
Nevermind I got it!

2. Originally Posted by cottongirl
$\frac{1}{x+3} + \frac{1}{x^2 + 5x +6}$

When I am getting a common denominator here, Should I factor the quadratic first or go ahead and multiply to get a common denominator?
Either way will work, but finding the factors first will make your steps simpler.

For instance, you can add 1/4 and 1/2 by first converting to a common denominator of 4*2 = 8: 1/4 + 1/2 = 2/8 + 4/8 = 6/8 = 3/4. But if you'd factored first and noted that 2 is a factor of 4, you could have converted to a least common denominator of 4: 1/4 + 1/2 = 1/4 + 2/4 = 3/4.

It works the same way with rational expressions (polynomial fractions).

3. ALWAYS, ALWAYS, ALWAYS, factor. Factoring is the most important and vital tool a mathematician can possess. If you had not factored this first you would have been senselessly multiplying a binomial by a trinomial and ended up with 6 terms in your denominator, whereas the common denominator would have become obvious had you simply factored the trinomial in the right term. I suggest that you try both ways and time yourself as you do it. It should become evident which is the most expedient way to do this problem.
By the way, Why do you call yourself cottongirl?