 Rational Expressions MathBitsNotebook.com Terms of Use   Contact Person: Donna Roberts  A rational expression is an expression that is the ratio of two polynomials. Rational expressions are algebraic fractions in which the numerator is a polynomial and the denominator is also a polynomial (usually different from the numerator). The polynomials used in creating a rational expression may contain one term (monomial), two terms (binomial), three terms (trinomial), and so on.

 Rational Expressions (monomial/monomial) Rational Expression (binomial/binomial) Rational Expression (binomial/trinomial)    Expressions that are not polynomials cannot be used in the creation of rational expressions.

For example: is not a rational expression, since is not a polynomial.  Since rational expressions represent division, we must be careful to
avoid division by zero.
If a rational fraction has a variable in its denominator, we must ensure that any
value (or values) substituted for that variable will not create a zero denominator.

If it is not obvious which values will cause a division by zero error in a rational expression,
set the denominator equal to zero and solve for the variable.

 Rational expression: Could it possibly be undefined? When? Rational expression: Could it possibly be undefined? When? Obviously, when x = 1, the denominator will be zero, making the expression undefined. Domain:  Set the denominator = 0 and solve. a2 - 4 = 0 a2 = 4 For this rational expression, we must limit the x's which may be used, to avoid a division by zero error, and leaving the expression undefined. For this rational expression, we must prevent two x-values from being used in the expression. Domain: Rational expression: Could it possibly be undefined? When? Rational expression: Could it possibly be undefined? When? Set: 8 - y = 0          8 = y Domain: All real numbers, except y = 8. Set: x2 + x - 12 = 0 (x - 3)(x + 4) = 0 x - 3 = 0;     x = 3 x + 4 = 0;    x = -4 Domain: All real numbers, but not x = 3 and not x = -4. NOTE: The re-posting of materials (in part or whole) from this site to the Internet is copyright violation and is not considered "fair use" for educators. Please read the "Terms of Use".