afreemanny said:

I just don't get this chapter! Here is a practice question I have:

Could someone show me each step so I can learn this right???

7a^2 - 42a

_________

a^3 - 4a^2 - 12a

A: Write the domain in set-builder notation.

B: Reduce the rational expression.

I don't know why I am doing this to myself!!! I am trying to learn this stuff to help my kids with their homework when I can and I am driving myself crazy!!!!!!!

Calm down; you sound like a heck of a good mother...

Start by taking the common "a" out ("a" is in every term):

a(7a - 42)

------------------

a(a^2 - 4a - 12)

Now you can cancel them out:

7a - 42

---------------

a^2 - 4a - 12

Are you still with me?

7a - 42 = 7(a - 6) : ok?

a^2 - 4a - 12 = (a - 6)(a + 2) : ok?

So now our fraction is:

7(a - 6)

----------------

(a - 6)(a + 2)

Now you can cancel out the (a - 6):

7

----

a + 2

So that was part B: "reducing the rational expression"; got that?

Not sure what's meant in part A;

the only restriction we now have on "a" is it can't = -2:

this would make the fraction's denominator a + 2 = -2 + 2 = 0 : a no-no

Hope I was able to help out, mom.