Dividing with Algebra

Date: 3/25/96 at 13:10:53
From: Carl Stromberg
Subject: Math problem

I have a big problem:

I shall factorize and reduce this problem:

(3x-9) / (2x-6)=
and
(x2+2xy) / (3x+6y)=  

I hope for answer!

Sincerely.
Carl Christian Stromberg, Norway

Date: 3/26/96 at 15:56:19
From: Doctor Patrick
Subject: Re: Math problem

Hi Carl!  

When you want to solve a problem like this, you need to look 
for two things.  The first thing to do is to is to look for numbers 
that will divide all the terms within one set of parentheses, and then 
a number that will divide the terms in the other set of parentheses.  
The second thing we need to do is to choose from the possible factors 
(if there are more than one) and find which one will give us a common 
factor in the parentheses.

For example, in the first problem you asked about, (3x-9)/(2x-6), we 
can factor a 3 out of the first set of terms, since both 3x and 9 are 
divisible by three.  This gives us 3(x-3).  The second set of terms can 
be factored by 2, giving us 2(x-3).  Do you see how that works?

The problem now is (3(x-3))/(2(x-3)).  Do you see any common term 
we can cancel out?

How about (x-3)?  If we divide the (x-3) in the numerator by the (x-3) 
in the denominator, we get 3/2, a much nicer number then what we 
started with.

I'll let you try the second problem on your own.  You can solve it in 
the same way.  First find numbers that can be factored out of the 
original terms.  Then divide out any common terms in the numerator 
and denominator.

Good luck

-Doctor Patrick,  The Math Forum