Problem 86 - College Algebra

Question

What is a rational expression?

Step-by-Step Solution

Answer

A rational expression is defined as an algebraic expression that can be written as a ratio of two polynomials. Like a ratio of two integers (a rational number), a rational expression is a ratio of two polynomial expressions. However, the polynomial in the denominator should not be zero because division by zero is undefined in mathematics.

Step 1: Understanding of Rational Numbers

First, it's vital to understand what rational numbers are. Rational numbers are numbers that can be expressed as fractions where the numerator is an integer and the denominator is an integer not equal to zero.

Step 2: Understanding Expressions in Mathematics

An expression in mathematics refers to a sequence of symbols that represents a quantity or an operator. Expressions do not contain equals signs.

Step 3: Definition of a Rational Expression

A rational expression is an algebraic expression that can be written as a ratio of two polynomials. Like a ratio of two integers (rational number), a rational expression is a ratio of two polynomial expressions. Note, in a rational expression the denominator should not be zero.