Question

Are a rational expression and its simplified forms equivalent?

Answer 1

http://openstudy.com/study#/updates/50fe199de4b0426c6367b15c

Answer 2

i was hoping to get a bettr answer because that was confusing lol

Answer 3

The problem is that the question is a little ambiguous. Here are 3 other answers, as you can see they are a little different.
https://answers.yahoo.com/question/index?qid=20130124071641AAcuTAX
http://openstudy.com/study#/updates/5108a7aae4b070d859be5e81
http://openstudy.com/study#/updates/5112a79be4b07c1a5a646faa

I'll try to give my own answer then.
The resource
http://tutorial.math.lamar.edu/Classes/Alg/RationalExpressions.aspx
states that:
"A rational expression is nothing more than a fraction in which the numerator and/or the denominator are polynomials."
which means it would be of the sort
$$
\frac{(x+3)(x-1)}{x-1}
$$
As the resource shows, this can be simplified in similar way to rational numbers. we can cancel common factors of the numerator and denominator. For example:
$$
\frac{16}{6} = \frac{8\cdot\cancel2}{3\cdot\cancel2} = \frac{8}{3}
$$This simplified ratio has the same value as the original.
So in our example:
$$
\frac{(x+3)\cancel{(x-1)}}{\cancel{x-1}} = x+3
$$
However, what's important to notice here is that in rational expressions we have to avoid division by zero.
That means that in our original expression x cannot be 1 because if it would be then the denominator \(x-1\) would be 0. This adds a requirement stating \(x\neq1\).
The simplified expression \(x+3\) doesn't involve a division, so the restriction on x is not explicit anymore.
So no, I wouldn't say that the simplified expression alone is equivalent to the original one.
$$
x+3 \;\;\;\;\;\; x\neq1
$$Would be.

Hope i'm clear

Answer 4

Oh okay I understand thank you!:))) have a nice day!