Like what you saw?
Create FREE Account and:
 Watch all FREE content in 21 subjects(388 videos for 23 hours)
 FREE advice on how to get better grades at school from an expert
 Attend and watch FREE live webinar on useful topics
Definition and Domain of a Rational Expression  Problem 3
Carl Horowitz
Carl Horowitz
University of Michigan
Runs his own tutoring company
Carl taught upperlevel math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
Whenever we simplify a rational expression, what we are looking for is the same thing in the numerator and the denominator if we have the same thing in both places we cancel them out to get rid of them. For this particular example what we have is 5 minus x over x minus 5, which look very similar however they are not exactly the same thing.
So what I want to do to show you this actually how is actually related is factor out a negative 1 out of one of them. It doesn’t matter which just chose one to factor out a 1. So I am going to factor out a 1 from the top.
Like I said it doesn’t matter you can do it just for the bottom as well and be just fine. So when we take that a 1 from 5 we end up with 5 and when we take out a 1 from –x, we end up with plus x and our denominator stays the same.
Doing a little bit of rearranging of this top phrase what we end up with is 1 times x minus 5 over x minus 5. So what you see is now we actually have the same thing so now we can cancel these out and leaving us with 1. These are what I call opposites I’m not exactly sure what the appropriate term is but I call them opposites because I cancel to 1.
Now what we are looking for is basically the same number where everything is the opposite sign. My 5 is positive up here my 5 is negative down here, x is positive here x is negative there. So long as everything Is opposite, you can cancel them. If we have say x minus 3 over x plus 3, there is nothing we can do with because our x’s are actually the same sign. Our 3’s are opposite but our x’s aren’t, so we can’t cancel it. It only works as if they are both opposites of each other. So when cancelling anything like this if our signs are switched we know we can cancel to 1.
Last thing I want to do with this example is talk about the domain. The domain is the values of x so we can plug in keeping in mind that we can’t divide by 0. So we always go to our original equation when we are finding the domain. If we went to a simplified version of 1 we can plug in anything but we need to go to our original statement which is 5 minus x over x minus 5. We can make the denominator 0 so x cannot be equal to 5
So that is how we deal with rational expressions when we are including opposites that cancel to 1.
Please enter your name.
Are you sure you want to delete this comment?
Carl Horowitz
B.S. in Mathematics University of Michigan
He knows how to make difficult math concepts easy for everyone to understand. He speaks at a steady pace and his stepbystep explanations are easy to follow.
i love you you are the best, ive spent 3 hours trying to understand probability and this is making sense now finally”
BRIGHTSTORM IS A REVOLUTION !!!”
because of you i ve got a 100/100 in my test thanks”
Sample Problems (4)
Need help with a problem?
Watch expert teachers solve similar problems.

Definition and Domain of a Rational Expression
Problem 1 5,927 viewsDomain for:
x − 3 x + 2 
Definition and Domain of a Rational Expression
Problem 2 4,737 viewsSimplify:
x − 1 x² − 4x + 3Domain: 
Definition and Domain of a Rational Expression
Problem 3 4,003 viewsSimplify:
5 − x x − 5Domain: 
Definition and Domain of a Rational Expression
Problem 4 3,870 viewsSimplify:
x² − 5x + 6 4 − x²Domain:
Comments (0)
Please Sign in or Sign up to add your comment.
·
Delete