1) a. radical in the numerator which means the variable does not have an integer exponent
b. division by a variable and therefore, the variable could be zero
c. division by zero
d. exponent that is a variable
2). Your list should include the examples from number 7: radicals, division by zero, variables as exponents, and division by a variable.
Note: If the numerator and/or denominator are not polynomials be definition, then the expression cannot be a rational expression.