Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
kaylala
Group Title
The rational expression
a^3  a^2

a^2  1
where a ≠ ±1 can be simplified as WHAT?
TOPIC: Rational Expressions
 one year ago
 one year ago
kaylala Group Title
The rational expression a^3  a^2  a^2  1 where a ≠ ±1 can be simplified as WHAT? TOPIC: Rational Expressions
 one year ago
 one year ago

This Question is Closed

whpalmer4 Group TitleBest ResponseYou've already chosen the best response.1
What happens if you factor the numerator of this expression? Do you see any common factors after you do so?
 one year ago

whpalmer4 Group TitleBest ResponseYou've already chosen the best response.1
\[a^3a^2 = a^2(a1)\]right?
 one year ago

whpalmer4 Group TitleBest ResponseYou've already chosen the best response.1
Nothing appears to be a common factor with the denominator, does it?
 one year ago

whpalmer4 Group TitleBest ResponseYou've already chosen the best response.1
What if you now factor the denominator?
 one year ago

kaylala Group TitleBest ResponseYou've already chosen the best response.0
yes. @whpalmer4 see the image: (but there could be 2 answers; see the top and bottom image)
 one year ago

whpalmer4 Group TitleBest ResponseYou've already chosen the best response.1
After you've factored both numerator and denominator you have the following: \[\frac{a^2(a1)}{(a1)(a+1)} = \frac{a^2\cancel{(a1)}}{(a+1)\cancel{(a1)}} = \frac{a^2}{a+1}\]
 one year ago

whpalmer4 Group TitleBest ResponseYou've already chosen the best response.1
the original restrictions on \(a\) still apply: \(a \ne \pm 1\)
 one year ago

kaylala Group TitleBest ResponseYou've already chosen the best response.0
oh ok thanks @whpalmer4 by the way, what original restrictions?
 one year ago

whpalmer4 Group TitleBest ResponseYou've already chosen the best response.1
\(a\ne \pm1\) if a=1 or a = 1, the denominator of the original expression would equal 0, and the result dividing by 0 is undefined...for the new expression, in theory we could have a = 1 without any problem (the denominator would equal 2, and dividing by 2 is a commonly accepted practice :) but we are trying to make a simpler but equivalent version of the original expression, and so to make it 100% equivalent, we have to put a=1 as offlimits, just as it was in the original.
 one year ago

whpalmer4 Group TitleBest ResponseYou've already chosen the best response.1
otherwise, it isn't equivalent — it's a function that is defined somewhere where the other one wasn't.
 one year ago

kaylala Group TitleBest ResponseYou've already chosen the best response.0
ah... okay thank you so much @whpalmer4
 one year ago

whpalmer4 Group TitleBest ResponseYou've already chosen the best response.1
you're welcome.
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.