A rational expression is of the form `(P(x))/(Q(x))` where P(x) and Q(x) are polynomials and Q(x) is not identically zero. (Note that x need not be a variable.) ((Also note that Q(x) can be zero for some values of x; just not every value of x.))

Rational expressions behave much as fractions do -- you add them by finding a common denominator, you multiply by multiplying numerator by numerator and denominator by denominator. And like fractions you can srite them as a "mixed number"; in this case as a polynomial plus a rational expression by using long division much like you would write a fraction as a mixed number by employing division.