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Chapter 0: Problem 86

What is a rational expression?

Short Answer

Expert verified
A rational expression is an algebraic expression that can be defined as the ratio of two polynomials, with the denominator not equal to zero.

Step by step solution

01

Understanding the concept of an Rational Expression

A rational expression, often referred to as a rational function, is any expression or function which includes a polynomial in its numerator and denominator. In short, it can be simply described as the ratio of two polynomials.
02

Recognizing a Rational Expression

A rational expression is typically presented in the form \(\frac{p(x)}{q(x)}\) where p(x) and q(x) are polynomials and q(x) is not equal to zero (as division by zero is undefined in mathematics). An example would be \(\frac{x^2 - 2x + 1}{x^2 + 3}\).
03

The Importance of Non-zero Denominators

One crucial point to note in a rational expression is that the denominator polynomial, q(x), should not result in zero. If it does, the rational expression is undefined. For example, in the rational expression \(\frac{2}{x-2}\), when x equals 2, the denominator becomes zero, making the entire expression undefined.

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Most popular questions from this chapter

Evaluate each algebraic expression for the given value or values of the variable(s). $$6+5(x-6)^{3}, \text { for } x=8$$

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