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
Joined
Feb 17, 2004
Messages
1,489
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
:D

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!" :oops:
 

Denis

Senior Member
Joined
Feb 17, 2004
Messages
1,489
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
Joined
Jan 28, 2005
Messages
5,588
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"
 
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