To **evaluate** a rational expression
at a particular value of each variable,
evaluate the numerator and denominator and divide the results.
The rational expression is **undefined**
whenever the bottom evaluates to 0.

A rational expression is **simplified**
if

- the top and bottom have only integer coefficients,
- the leading coefficient on the bottom is positive,
- the coefficients have no common integer factor greater than 1, and
- the top and bottom have no common polynomial factor that is not constant.

We add, subtract, multiply, and divide rational expressions using the same techniques as for rational numbers. But systematic factoring is now more important, since less can be done by trial and error.

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This web page was written between 2010 and 2015 by Toby Bartels, last edited on 2015 July 13. Toby reserves no legal rights to it.

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