Question

In the following exercises, determine the values for which the rational expression is undefined. (a) $\frac{2 x}{z}$ (b) $\frac{4 p-1}{6 p-5}$ (c) $\frac{n-3}{n^{2}+2 n-8}$

Name: Problem 1, Chapter 8: Elementary Algebra
Uploaded: 2021-07-14T16:08:06-08:00
Duration: 2 min 27 s
Channel: Chris Wojturski
Description: In the following exercises, determine the values for which the rational expression is undefined. (a) (2 x)/(z) (b) (4 p-1)/(6 p-5) (c) (n-3)/(n^2+2 n-8)

   In the following exercises, determine the values for which the rational expression is undefined.
(a) $\frac{2 x}{z}$
(b) $\frac{4 p-1}{6 p-5}$
(c) $\frac{n-3}{n^{2}+2 n-8}$

Elementary Algebra

Lynn Marecek 1st Edition

Chapter 8, Problem 1

Instant Answer

Solved by Expert Chris Wojturski

07/14/2021

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A rational expression is undefined when its denominator is equal to zero. Show more…

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In the following exercises, determine the values for which the rational expression is undefined. (a) $\frac{2 x}{z}$ (b) $\frac{4 p-1}{6 p-5}$ (c) $\frac{n-3}{n^{2}+2 n-8}$

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Key Concepts

Solving Equations for Zeros

To find where a rational expression is undefined, one sets the denominator equal to zero and solves the resulting equation. This process may require solving linear or quadratic equations, and sometimes factoring the polynomial, to identify the specific values that must be excluded from the domain.

Domain Restrictions

Domain restrictions in the context of rational expressions refer to the values of the variable that make the denominator zero. These restrictions arise because division by zero is undefined in mathematics. Identifying these restrictions is essential for determining the set of permissible values for the expression.

Rational Expression

A rational expression is a fraction where both the numerator and the denominator are polynomials. Understanding these expressions involves recognizing that they are defined for all values of the variable except where the denominator equals zero.

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