Welcome to Georgia Highlands College Math 97 and Math 99 tutorial videos.
In this video segment, we’ll answer the question, what does it mean for a
rational expression to be simplified.
Well a rational expression is simplified if its’ numerator and denominator have
no common factors besides one.
Let’s take a look at a principle and an example to help us understand this.
All right, so we have the fundamental principle of rational expressions that
states if P, Q, and R, are polynomials. So we have two polynomials being
multiplied in the numerator and two polynomials being multiplied in the
denominator and Q and R are not zero, because if Q and R, if either of them were
zero you know we would have an undefined situation.
So if we have this situation set up, then we know that P times R over Q times R
will equal P over Q.
Now let’s see how that actually happens. So we start out with PR/QR and we could
rewrite that rational expression by pulling those fractions that are being
multiplied apart and say that that’s the same thing as P/Q times R/R because we
know when we multiply fractions we just multiply straight across. So we can pull
them back apart and put the multiplication symbol between them.
Well, anything divided by its’ self is just one. So when we do so, we really
have the situation of P/Q being multiplied by one and anything times one is just
itself.
So this is the fundamental principle of rational expressions that will help us
simplify our rational expressions, pulling out all common factors besides one.
In the next video, we’ll see how to actually go about doing this process of
simplifying rational expressions using the fundamental principle of rational
expressions.
I hope that this has been helpful for you in beginning to understand how to work
with rational expressions and how to begin simplifying them by pulling out
common factors.
If you have any other questions about this process, please contact your
Highlands instructor.
Thank you
