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Chapter 0: Problem 70

What is a rational expression?

Short Answer

Expert verified
A rational expression is a mathematical expression that is the ratio of two polynomials. An example is \(\frac{3x^2 - 2x + 7}{x^3 - 1}\). The polynomial in the denominator should not be zero.

Step by step solution

01

Define Polynomial

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer powers of variables. An example of a polynomial is \(3x^2 - 2x + 7\).
02

Define Ratio

A ratio is a relationship between two numbers of the same kind. In mathematics, it is simply a fraction where we divide one quantity by another quantities of the same unit. An example is the ratio between 4 and 7, which can be written as \(\frac{4}{7}\).
03

Define Rational Expression

A rational expression, as per the definitions in Step 1 and 2, is an expression of the ratio of two polynomials, where the polynomial in the denominator is not zero. An example of a rational expression is \(\frac{3x^2 - 2x + 7}{x^3 - 1}\).

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Most popular questions from this chapter

In Exercises \(1-10\), factor out the greatest common factor. $$4 x^{2}-8 x$$

In Exercises \(1-10\), factor out the greatest common factor. $$16 x-24$$

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Simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. $$ \frac{4 x-8}{x^{2}-4 x+4} $$
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