Find the Domain: When the Denominator 2x-6 Affects the Rational Equation

To find the domain of the expression $\frac{5x+8}{2x-6} = 30$, we need to identify values of $x$ that make the denominator of the fraction zero.

Step 1: Identify the denominator of the fraction, which is $2x - 6$.

Step 2: Set the denominator equal to zero to find the values to exclude:

• Solve the equation $2x - 6 = 0$.
• Add 6 to both sides: $2x = 6$.
• Divide both sides by 2: $x = 3$.

Therefore, $x = 3$ is the value that makes the denominator zero, so it must be excluded from the domain.

Given the choices, the correct answer is $x \neq 3$.

Therefore, the domain of the expression is all real numbers except $x = 3$.

This implies that the correct choice is:

$x \neq 3$