Question

Define a rational expression. Then give an example of a rational expression.

Short answer

A Rational Expression is any expression that can be expressed as a fraction of two polynomials. The denominator should not be equal to zero. An example is \( \frac{x^2 - 1}{x + 2} \).

Step-by-step solution

Definition of a Rational Expression

A Rational Expression is any expression which can be expressed as a ratio (or fraction) of two polynomials. An important thing to note is that the denominator (the polynomial in the bottom of the fraction) should not be equal to zero, as division by zero is undefined.

Example of a Rational Expression

An example of a Rational Expression is \( \frac{x^2 - 1}{x + 2} \). Here, \(x^2 - 1\) and \(x + 2\) are both polynomials, and the denominator \(x + 2\) is not equal to zero for every value of \(x\). Which makes \(\frac{x^2 -1}{x + 2}\) a valid example of a rational expression.