A rational expression is defined as?

A rational expression is defined as?

• A. A fraction where numerator and denominator are polynomials; the denominator cannot be zero.
• B. A difference of two monomials.
• C. A product of a polynomial and a constant.
• D. A polynomial divided by a constant.

Answer: (A)

A rational expression is a ratio of two polynomials in the variable, with the denominator not equal to zero. This means you can write it as P(x) over Q(x), where P and Q are polynomials and Q(x) ≠ 0 for all x in the domain. That’s exactly what the option says: a fraction whose numerator and denominator are polynomials, and the denominator cannot be zero. The other descriptions don’t capture the idea of a ratio of polynomials in the variable: a difference of monomials isn’t a fraction; a product of a polynomial and a constant is just a polynomial; and a polynomial divided by a constant is a special, simpler case that doesn’t emphasize the general form of a rational expression.

A rational expression is a ratio of two polynomials in the variable, with the denominator not equal to zero. This means you can write it as P(x) over Q(x), where P and Q are polynomials and Q(x) ≠ 0 for all x in the domain. That’s exactly what the option says: a fraction whose numerator and denominator are polynomials, and the denominator cannot be zero.

The other descriptions don’t capture the idea of a ratio of polynomials in the variable: a difference of monomials isn’t a fraction; a product of a polynomial and a constant is just a polynomial; and a polynomial divided by a constant is a special, simpler case that doesn’t emphasize the general form of a rational expression.