# How do you state the excluded values for rational expressions?

Jan 21, 2015

The only rule with rational expression is that the denominator can't be zero, since you can't divide by zero.

Remember that an expression is said to be rational only if variables appear at the denominator: thus $\setminus \frac{\setminus \cos \left(x\right) + 3 {x}^{2}}{2}$ is NOT a rational expression.

If you actually have an expression in which variables appear at the denominator, you must exclude the values of the variables for which the expression at the denominator becomes 0. In formulas, if you have an expression like $\setminus \frac{f \left(x\right)}{g \left(x\right)}$, such an expression is defined for all $x$ such that $g \left(x\right) \setminus \ne 0$.