Chapter 6, Problem 1RE

To determine

To calculate: The value of the variable that will be excluded in the rational expression $\frac{2}{x-4}$.

Answer to Problem 1RE

Solution:

The value of the variable that will be excluded in the rational expression $\frac{2}{x-4}$ is $4$.

Explanation of Solution

Given Information:

The provided rational expression is $\frac{2}{x-4}$.

Formula used:

The set of all the values on which the denominator q of the rational function $f\left(x\right)=\frac{p}{q}$ is non-zero is called domain of that rational function.

The point at which the value of the rational expression is zero that will be the excluded value of the variable of that rational expression.

Calculation:

Consider the rational expression, $\frac{2}{x-4}$

Equate denominator to $0$. So equation will be,

$x-4=0$

Solve for x,

$\begin{array}{c}x-4=0\\ x=4\end{array}$

Thus, domain of $\frac{2}{x-4}$ is real number but $x\ne 4$ or $x=\left(-\infty ,4\right)\cup \left(4,\infty \right)$.

Therefore, the value of the variable that will be excluded in the rational expression $\frac{2}{x-4}$ is $4$.