A rational expression
is made of two polynomial expressions:
the numerator (or top)
and the denominator (or bottom),
where the denominator is not the constant polynomial 0.
Think of a rational expression as a fraction:
the numerator divided by the denominator.
Every polynomial may be interpreted as a rational expression
whose denominator is the constant polynomial 1.
To evaluate a rational expression
at a particular value of each variable,
evaluate the numerator and denominator and divide the results.
The rational expression its undefined
whenever the bottom evaluates to 0.
A rational expression is simplified
We can simplify rational expressions by factoring the top and bottom
and cancelling and common factors;
we may then leave the expression in factored form.
(If the leading coefficient in the numerator is negative
and we leave the expression in factored form,
then we usually place the minus sign in front of the entire expression.)
- the top and bottom have only integer coefficients,
- the leading coefficient on the bottom is positive,
- the coefficients have no common factor greater than 1, and
- the top and bottom have no common factor that is not constant.
We add, subtract, multiply, and divide rational expressions
using the same techniques as for rational numbers.
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This web page was written in 2010 and 2011 by Toby Bartels,
last edited on 2011 October 17.
Toby reserves no legal rights to it.
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