Chapter A.1, Problem 73AYU

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 73AYU

$x=\text{ 0}$, $x=\text{ 1}$ and $x=-1$.

Explanation of Solution

Given:

$\frac{x^2+5x-10}{x^3-x}$

Calculation:

$x^3-x=0$

$x\left(x^2-1\right)=0$

$x=0,x^2-1=0$

$x=0,x=-1,x=1$

The domain of the variable $x$ in the expression $\frac{x^2+5x-10}{x^3-x}$ is $\left\{x\text{|}x\ne \text{ 0, }\pm 1\right\}$, since, if $x=\text{ 0, }\pm 1$, the denominator becomes 0, which is not defined. Hence answer is $x=\text{ 0}$, $x=\text{ 1}$ and $x=-1$.