# What is the meaning of rational algebraic expression?

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.

### What is the rational algebraic expressions?

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.

### How different is the rational algebraic expressions to not rational algebraic expressions?

Basically, a rational expression would include only additions, subtractions, multiplications, divisions, and integer powers, while an irrational expression could, in addition, include several additional functions, such as roots (or equivalently, non-integer powers), exponential functions, logarithms, trigonometric functions, and just about any other function.

### Are all polynomials algebraic expressions?

From Wikipedia: "In mathematics, an algebraic expression is an expression built up from constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)". So, the answer is yes - since any polynomial can be obtained by applying only a subset of these operations (additions, subtraction, multiplication).

### How can a rational algebraic expressions be simplified?

For example if it was y+y+y it would be 3y. or 3x+2y-1x= (3-1)x + 2y = 2x + 2y = 2(x+y) I'm not sure that the above addresses the question of rational algebraic expressions. You can simplify by finding common factors between numerator and denominator, or try long division, if no factors are evident. See the related link for "How do you divide rational algebraic expression"