# Rational expressions

G

#### Guest

##### Guest
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!!!!!!!

#### Denis

##### Senior Member
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.

G

#### Guest

##### Guest

My son tends not to agree sometimes. He is a honor student and I make him spend an hour on school work of some kind even through the summer. Bummer for him...but. thanks for telling me to calm down. I do tend to get myself wound up a time or two. :roll:

G

#### Guest

##### Guest
Getting there slowly

Will take me time, but at least you helped break it down. The "darn" book just says "hey, this is the way it is...deal with it!"

#### Denis

##### Senior Member
A note on "cancelling out", Amy:
numerator and denominator must be in multiplication format, like:

a*b*c*d*e
------------
f*c*g*d

Notice that c and d are in both numerator and denominator;
you can cancel those out to get:

a*b*e
-------
f*g

That's in multiplication format:
(a+b)
--------------
(a+b)(a+c)

means 1 times (a+b) divided by [(a+b) times (a+c)]
so the (a+b) cancels out, leaving:

1
------
a + c

Don't forget that 1 remains as numerator.

Hope that helps.

#### soroban

##### Elite Member
Hello, afreemanny!

Denis is absolutely correct . . . here's my version of the same thing.

. . . . 7a<sup>2</sup> - 42a
. . ----------------
. . a<sup>3</sup> - 4a<sup>2</sup> - 12a

A: Write the domain in set-builder notation.
B: Reduce the rational expression.
When I see "a polynomial over a polynomial", my first instinct is to FACTOR.
. . (Usually, they design the problem so something will cancel out.)

. .Numerator: . 7a<sup>2</sup> - 42a . = . 7a(a - 6)

Denominator: . a<sup>3</sup> - 4a<sup>2</sup> - 12a . = . a(a<sup>2</sup> - 4a - 12a) . = . a(a + 2)(a - 6)

. . . . . . . . . . . . . . . . . . . . . 7a(a - 6)
The fraction becomes: . ------------------
. . . . . . . . . . . . . . . . . . . a(a + 2)(a - 6)

If we promise that a ≠ 0 and a ≠ 6, we can cancel.

. . . . . . . . . . . . .7
. . . and get: . ------ .
. . . . . . . . . . . a + 2

. . . and we have another restriction: .a ≠ -2

[A] .The domain is: . {a ε R | a ≠ 0, a ≠ 6, a ≠ -2}

G

#### Guest

##### Guest
A wish

I wish I understood math like you all. Thanks so much for your help.
"A crazy mom"