What are rational expressions defined as?

What are rational expressions defined as?

• A. Fractions with polynomials in both numerator and denominator
• B. Polynomials with integer coefficients
• C. Arithmetic expressions involving only whole numbers
• D. Fractions with integers only

Answer: (A)

Rational expressions are defined as fractions that have polynomials in both the numerator and the denominator. This means that both the top and bottom parts of the fraction can be complex algebraic expressions made up of variables and constants, as long as they are structured like polynomials. For instance, an expression such as (2x^2 + 3x - 5) / (x - 4) qualifies as a rational expression because both the numerator (2x^2 + 3x - 5) and the denominator (x - 4) are polynomials. This definition is essential in algebra because it allows for a wide variety of mathematical operations, such as simplification, addition, or multiplication of these expressions. The other options provided do not encapsulate the full definition of rational expressions. Polynomials with integer coefficients refer specifically to a type of polynomial but do not emphasize the requirement for the denominator as necessary for defining rational expressions. Arithmetic expressions involving only whole numbers and fractions with integers only are too limited and do not include the polynomial aspect necessary to define rational expressions accurately.

Rational expressions are defined as fractions that have polynomials in both the numerator and the denominator. This means that both the top and bottom parts of the fraction can be complex algebraic expressions made up of variables and constants, as long as they are structured like polynomials.

For instance, an expression such as (2x^2 + 3x - 5) / (x - 4) qualifies as a rational expression because both the numerator (2x^2 + 3x - 5) and the denominator (x - 4) are polynomials. This definition is essential in algebra because it allows for a wide variety of mathematical operations, such as simplification, addition, or multiplication of these expressions.

The other options provided do not encapsulate the full definition of rational expressions. Polynomials with integer coefficients refer specifically to a type of polynomial but do not emphasize the requirement for the denominator as necessary for defining rational expressions. Arithmetic expressions involving only whole numbers and fractions with integers only are too limited and do not include the polynomial aspect necessary to define rational expressions accurately.