A rational expression is simply a fraction whose numerator and/or denominator are polynomials. Its name is derived from being the ratio of two polynomials.
A polynomial is an expression made up of variables and constants, but only the operations of multiplication, addition and subtraction can be used, as well as non-negative integer exponents. In polynomials, division of constants is allowed, but no division by a variable.
An example of a rational expression would be: (x2 +4)/(x+1). When simplifying rational expressions, you should first factor both the numerator and denominator to see if there are any like expressions that will cancel out.