A rational algebraic expression is the ratio of two polynomials, each with rational coefficients. By suitable rescaling, both the polynomials can be made to have integer coefficients.
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an algebraic expression is an expression built up from constants, variables, and a finite number of algebraic operations (addition, subtraction, multiplication,division and exponentiation to a power that is a rational number). For example,
something that looks like ax^2+bx+c
A rational expression is an expression that includes only additions, subtractions, multiplications and divisions. Some of the things that will make an expression irrational (not rational) are square roots, higher-level roots, non-integer powers, exponentials (powers in which the variable expression occurs in the exponent), and common functions such as logarithms or trigonometric functions.