Determine the Domain of the Fraction Equation: 5x/(2(x-7)) = 10/(8x)

To find the domain of the rational equation $\frac{5x}{2(x-7)} = \frac{10}{8x}$, we need to ensure neither denominator equals zero.

Start by examining the first denominator, $2(x-7)$:

• Set $2(x-7) = 0$.
• Solve for $x$ to find $x - 7 = 0$, resulting in $x = 7$.

Next, examine the second denominator, $8x$:

• Set $8x = 0$.
• Solve for $x$ to find $x = 0$.

Therefore, the function is undefined at $x = 0$ and $x = 7$. These values should be excluded from the domain.

Thus, the domain of the given rational equation is all real numbers except where $x = 0$ and $x = 7$.

This corresponds to the correct answer choice: $x \neq 0, x \neq 7$.