- radical in the numerator which means the variable does not have an integer exponent
- division by a variable and therefore, the variable could be zero
- division by zero
- exponent that is a variable
- Your list should include the examples from number 1: radicals, division by zero, variables as exponents, and division by a variable.
Note: If the numerator and/or denominator are not polynomials by definition, then the expression cannot be a rational expression.