Simplify the following expression if possible x^2-12(2x-12)/144-x^2

Question

Simplify the expression x^2-12(2x-12)/144-x^2

Answer 1

Hi, Kimberly.

I think you are asking about this problem:

x^2 - 12 (2x - 12)
  144 - x^2

When you are simplifying rational polynomial expressions, start with simplifying each part of the fraction.  If you can distribute, combine like terms, or factor anything, you should.  So let's take a look at each part:

Numerator:  x^2 - 12 (2x - 12)

Let's distribute the neg 12 over the grouping to get: x^2 - 12x + 144
Next, using the idea of FOIL (but in reverse), factor this trinomial into two binomial factors:
(x - 12)(x - 12)

Denominator:  144 - x^2

First, rewrite this expression in descending order of exponents:  - x^2 + 144
Recognize, that since the leading term (x^2) is negative, factor out a GCF of neg 1:  - (x^2 - 144)
Now, do you see that we have a difference of two squares in the grouping?  We can factor further:
- (x + 12)(x - 12)

Once you've simplified each part of your fraction, you may start cancelling whole factors:

  (x - 12)(x - 12)                                                        .
- (x + 12)(x - 12)

Do you see that one of the numerator's two (x - 12) factors can cancel with the denominator's (x - 12) factor?  When we do that, we have an express that has a neg sign in the denominator.  When you write your answer, just place the negative sign in front of the whole expression:

       x - 12
 -    ______
       x + 12

Hope this helped you with simplifying this type of expression.