Expert: David Montiel - 8/17/2009

Question
QUESTION: i have no idea how to solve this problem! please please please help me!

if r does not equal + or - 2,  r^2-5r+6 over r^2-4=?

ANSWER: Dear Jennifer,

I have the policy of not giving the full solution to problems, but I'll be glad to help you get started.

In the first part, the question states that "r" can't take the values -2 or +2. The reason for this is that, if you substitute any of these numbers in the denominator you get zero. This leads to an indetermination because
[anything]/0 is not defined, but you should not worry about that for now.

What you're supposed to do is simplify the polynomial division r^2-5r+6 over r^2-4, that is, write it as a more simple expression. A useful strategy is to factorize both numerator and denominator. What I mean by this is: try to write each of them as a product of the form:

         (r + a)*(r + b)  

...that should help to simplify things.

I hope this is useful.
David

---------- FOLLOW-UP ----------

QUESTION: Thanks for your help, but I still don't understand what you mean when you say write each of them as a product of the form: =/

Answer
What I meant is writing a polynomial as the multiplication of binomials. Let me give you some examples:

x^2 + 4x + 4 = (x+2)(x+2) = (x+2)^2    <==== factorized form   (x+2 is a binomial)

another one:

x^2 - 3x + 2  = (x-2)(x-1)       <==== factorized form

and yet another one:

x^2 - 9  = (x+3)(x-3)       <==== factorized form


In all cases above, the right hand side (the factorized form) looks like (x + a)*(x + b)... of course, with different values of "a" and "b" for each case.

Is this clearer now? Please let me know if it isn't.
Cheers,
David