The definition of rational expressions and their domains are examined.
Definition
A rational expression is the quotient of two polynomials.
Examples of Rational Expressions
Domain of Rational Expressions
It is clear that the above expressions are undefined if a division by 0 occurs. The domain of a rational expression excludes all values that make the denominator equal to 0.

The domain of the rational expression
(x  1) / (x + 2)
is the set of all real numbers except x =  2

The domain of the rational expression
(x + 1) / ((x + 2)(x  3))
is the set of all real numbers except x = 2 and x = 3

The domain of the rational expression
1 / (x^{2} + 1)
is the set of all real numbers since the denominator x^{2} + 1 cannot be 0 for any real number x.

To find the domain of the rational expression,
(x^{2} + 4) / (x^{3} + 2 x^{2}  3 x)
we first have to factor the denominator and find its zeros.
x^{3} + 2 x^{2}  3 x = x(x^{2} + 2 x  3)
= x(x  1)(x + 3)
The domain of the above rational expressions is the set of all real numbers except x = 0, x = 1 and x =  3.
Exercises
Find the domain of each of the Rational Expressions given below.
Answers to the above exercises
More references to topics related to rational expressions.
