Chapter 11, Problem 22GR

To determine

Find the way we can express the rational expression as a ratio of two expressions.

Answer to Problem 22GR

Explanation of Solution

Given:

When people are rational they make sense. When a number is rational, it can be written as the ratio of two integers. Do you think that the term rational expression refers to an expression that makes sense or to an expression that involves a ratio?

Concept Used:

A rational number is any number that can be expressed as a ratio of two integers (hence the name "rational").

For example, 1.5 is rational since it can be written as $\frac{3}{2}\text{or}\frac{9}{6}\text{or}\frac{18}{12}$ or another fraction or two integers.

A rational expression is simply a quotient of two polynomials. Or in other words, it is a fraction whose numerator and denominator are polynomials.

Yes, as a rational expression is simply a quotient of two polynomials, it can be written as ratio of two expressions.

Example: $\frac{x+2}{x+6}\text{or}(x+2):(x+6)$