Michelle S. answered • 03/16/13

Rx for Success in Math and Science

First, simplify the expressions by factoring them out. For example, a^{2 }+ 7a + 6 becomes (a + 6) (a+1).

If you do this, the fraction then looks like this:

(a+6) (a+1) times (a +4) (a -2)

(a+5)(a-2) (a+1) (a+1)

You may then cancel out a factor that appears in both either numerator and either denominator, just as you can cancel out numeral factors that way. In this case, (a-2) appears in the numerator of the second fraction and the denominator of the first fraction, and these can be cancelled out. Also, (a+1) appears in the numerator of the first fraction and twice in the denominator of the second fraction. One of the (a+1)'s only can be cancelled in the denominator, along with the one in the numerator. I don't know how to make the cancel marks here, but you are then left with the following expression when you multiply them as you would any other fraction. (Numerator x Numerator and Denominator x Denominator):

(a+6) (a+4)

(a+5) (a+1)

Most teachers/books I know would have you leave it in this form, but sometimes they want you to multiply it back out. Check to see.

The other thing you should be aware of, and will probably be asked to state in your answer, is that canceling off factors this way means that the denominator factor can never equal 0, or the fraction becomes undefined. You should take a look at the cancelled factors and determine what values for x would make that expression equal 0. In this case, a cannot be -1 or 2. You should write this out after the expression above, by adding a comma and a (cannot equal is an equal sign with a slash through it; I don't know how to create that here) -1 or 2.

If you have any trouble coming up following these steps and coming up with the same answers, please e-mail me to help with those steps.