Chapter A.1, Problem 74AYU

To determine

Which of the values (a) through (d), if any, must be excluded from the domain of the variable in each expression.

a. $x=3$   b. $x=\text{ 1}$   c. $x=\text{ 0}$   d. $x=-1$ 

Answer to Problem 74AYU

$x=\text{ 0}$

Explanation of Solution

Given:

$\frac{-9x^2-x+1}{x^3+x}$

Calculation:

$x^3\text{ + }x=0$

$x\left(x^2\text{ + }1\right)=0$

$x=0,x^2\text{ + }1=0$

The domain of the variable $x$ in the expression $\frac{-9x^2-x+1}{x^3+x}$ is $\left\{x\text{|}x\ne 0\right\}$, since, if $x=\text{ 0}$, the denominator becomes 0, which is not defined. Hence answer is $x=\text{ 0}$.