Learn math, science, English SAT & ACT from
highquaility study
videos by expert teachers
Learn math, science, English SAT & ACT from
highquaility study videos by expert teachers
Next video playing in 10
Definition and Domain of a Rational Expression  Problem 3
Cancel More videos
Definition and Domain of a Rational Expression  Problem 2
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!
So in order to simplify a rational expression what we want to do is cancel off anything that is in both the numerator and the denominator. Think about a fraction is you have 2 over 4, you can divide the top by 4, 2 in the bottom by 2 and you end up with one half. It's a similar concept writing it as simpler terms.
So how we do this is we just want to factor our numerator and our denominator. Numerator in this case we cannot cancel, so we are just left with x minus 1, and the denominator we want to factor out. It’s a trinomial we know we have x and x, our middle term is negative our last term is positive which tells us we have minus and minus and the only factors of 3 are 3 and 1.
So now we have x minus 1 in both the top and the bottom we can go ahead and cancel those out leaving us with 1 over x minus 3. So by factoring in common like factoring and cancelling like terms we are able to simplify this rational expression.
The other part of this question is asking about the domain. What values of x can we put to this expression and a common mistake that people do is they actually go to your simplified expression to find what your domain is. That’s not actually true what you have to do is go to your original statement before you cancel anything out.
So what we had is x² minus 4x plus 3 factors to this right here x minus 3 times x minus 1. This is where we have to look out to find out our domain. So this can’t be equal to 0 which tells our domain is everything but 1 and 3. These are almost equivalent statements except for the fact that we can’t plug in 1 into here, sorry we can’t plug 1 into here and we can’t plug 1 into here.
So whenever you are finding the domain for a rational expression you always want to go to the precancelled form even though these are fair
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.
Sample Problems (4)
Need help with a problem?
Watch expert teachers solve similar problems.

Definition and Domain of a Rational Expression
Problem 1 6,683 viewsDomain for:
x − 3 x + 2 
Definition and Domain of a Rational Expression
Problem 2 5,317 viewsSimplify:
x − 1 x² − 4x + 3Domain: 
Definition and Domain of a Rational Expression
Problem 3 4,448 viewsSimplify:
5 − x x − 5Domain: 
Definition and Domain of a Rational Expression
Problem 4 4,326 viewsSimplify:
x² − 5x + 6 4 − x²Domain:
Comments (0)
Please Sign in or Sign up to add your comment.
·
Delete