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Chapter 0: Problem 86

What is a rational expression?

Short Answer

Expert verified
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 by step solution

01

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.
02

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.
03

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.

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. First factoring out the greatest common factor makes it easier for me to determine how to factor the remaining factor, assuming that it is not prime.

Factor completely. $$ x^{4}-y^{4}-2 x^{3} y+2 x y^{3} $$

Evaluate each expression without using a calculator. $$27^{\frac{1}{3}}$$

What does \(a^{\frac{m}{n}}\) mean?

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Suppose a square garden has an area represented by \(9 x^{2}\) square feet. If one side is made 7 feet longer and the other side is made 2 feet shorter, then the trinomial that models the area of the larger garden is \(9 x^{2}+15 x-14\) square feet.
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