Determine which expressions are polynomials and which are not. The term "polynomial" refers to a finite expression which consists of both constants and variables. Polynomial expressions may only use addition, subtraction, multiplication and non-negative integer exponents. Polynomials can include expressions such as x^2 - 4x + 7 and x^3 + 2x - 1.
Define rational expressions. The term "rational expression" refers to mathematical equations which result in a ratio using two polynomials. Essentially it is a fraction which includes polynomials. Expressions such as (x + 2) / (x + 5) and (x^2 + 2x - 4) / 5x are both rational equations. Even the polynomial 4x^2 + 5 can be a rational expression as it can also be written as (4x^2 + 5) / 1.
Identify expressions which are not rational. Expressions which do not use polynomials would not be considered rational. Expressions such as (2 / x) / 4x and (1x + 5) / (3 - x^1/2) are not rational as they include non-polynomial expressions.
Create your own polynomials and rational expressions. Once you have a clear understanding of what polynomials and rational expressions are, and are not, you can begin writing out your own and seeing whether they qualify or not.
Practice using your own polynomials and rational equations. As always in math, learning comes through repetition and polynomials and rational equations can be learned through practice whatever materials are available.