Analyzing Domain in Rational Equation: 14/x - 6x = 2/(x-5)

To find the domain of the given function, we need to determine where the function is undefined due to division by zero. The function in question is:

$\frac{14}{x} - 6x = \frac{2}{x-5}$

We identify two fractions: $\frac{14}{x}$ and $\frac{2}{x-5}$. Each fraction has a denominator that can potentially cause division by zero:

• For $\frac{14}{x}$, the denominator $x$ shouldn't be zero. Thus, $x \neq 0$.
• For $\frac{2}{x-5}$, the denominator $x-5$ shouldn't be zero. Thus, $x \neq 5$.

By excluding these values from the set of all real numbers, we obtain the domain of the function. Therefore, the domain consists of all real numbers except for $x = 0$ and $x = 5$.

Thus, the domain of the function is $x \neq 0, x \neq 5$.