Welcome to Georgia Highlands College Math 97 and Math 99 tutorial videos.
In this video segment we’ll be answering the question, how do you simplify a
rational expression.
Well, the first step in this process is to factor both the numerator and the
denominator completely and secondly, you're going to come back and divide any of
the common factors out of both the numerator and the
denominator. Because remember, anything divided by itself is equal to one.
Let's take a look at an example.
So we have the example here of 7X plus 28 divided by 21X.
And before we actually get started in the simplification process, I just want to
note that should you want to evaluate this expression by plugging in values for
X, we do have an excluded value which we talked about in another video.
So before we get started simplifying we just want to note any excluded values.
So we set up the situation of the denominator equaling zero to figure out what
values we will not be able to plug in for X in this expression.
And you can see 0 divided by 21 gives 0, so just as a side note,
0 is the excluded value for this rational expression. But let's go ahead and
proceed with simplifying this rational expression by going through the two steps
that we just talked about.
The first step is to factor the numerator and the denominator completely.
Looking at the numerator, we see that we have a GCF of 7, there is a 7 in both
7X and 28 and when we divide that GCF out of both terms, we are left with X plus
4.
Now if we move to the denominator, we can rewrite 21 times X in its’ prime
factored form, which would just be 3 times 7 times X.
So 
we have both the numerator and the denominator factored.
The second step in this process is to divide both the numerator and the
denominator by any common factors. So it should be apparent that we can divide 7
by 7 leaving multiplying by one when we divide that out.
And simplifying this process we get X plus 4 divided by 3X.
So this is the simplified form of this rational expression. See all we did was
factor the numerator and denominator, divided out any common factors between the
numerator and the denominator, and then we’re left with the simplified rational
expression.
Now there are many different types of rational expressions, meaning that you
could have numerous different polynomials in the numerator and the denominator,
so you have to know your factoring methods to be able to simplify rational
expressions.
So make sure if you're a little rusty on your factoring, to go back and watch
the factoring videos before you move forward with simplifying rational
expression.
I hope this has been helpful for you though in laying out a process of
factoring and then dividing out common factors.
If you have any other questions about this process, please contact your
Highlands instructor.
Thank you.
