Factoring Fractions

Date: 12/7/95 at 19:12:41
From: Anonymous
Subject: dividing polynomials by monomials

12ax+16x
________   =  ?
    4x

I just don't understand how to do this.

Date: 12/23/95 at 22:28:55
From: Doctor Elise
Subject: Re: dividing polynomials by monomials

Hi!

The best way to tackle this one is to try factoring the first 
polynomial.

You start with

12ax + 16x

The first thing I notice, is that both expressions 
have an 'x' in them, so we can pull it out like this:

x(12a + 16)

(I've grouped the expressions together and multiplied the group 
by 'x', after dividing each expression by 'x').

Next, I look at 12 and 16, (especially since I already
know I have to divide by 4x) and realize they're both
divisible by 4, so I can pull the 4 out the same way, and I get:

4x(3a + 4)

Now the problem is easy, because I have 4x times something
divided by 4x, and the 4x's cancel each other out (because anything
divided by itself is 1)

so I end up with 4x(3a + 4)
                  __________   = 3a + 4
                       4x

Does this help?  Whenever you get a problem like this, the first
thing to try is to see if the part you're dividing by (the '4x', in 
this case) is a factor of each expression in the numerator.

You'd do the same thing if you had (3 * 2 * 5) + (3 * 7)
                                    ___________________
                                             3

You'd know to look for '3' as a common factor in each expression.

Extra Credit:

Can you find the answer to the problem I just posed?

- Doctor Elise,  The Geometry Forum