For which of the following values of $x$ is the rational expression undefined?
$\frac{7}{x-3}$

• A. $0$
• B. $-3$
• C. $3$
• D. $7$

Answer: (C)

Verified step by step guidance

1. Identify the rational expression given: \(\frac{7}{x - 3}\). A rational expression is undefined when its denominator equals zero because division by zero is undefined.
2. Set the denominator equal to zero to find the values of \(x\) that make the expression undefined: \(x - 3 = 0\).
3. Solve the equation \(x - 3 = 0\) by adding 3 to both sides: \(x = 3\).
4. Conclude that the rational expression \(\frac{7}{x - 3}\) is undefined when \(x = 3\) because the denominator becomes zero at this value.
5. Therefore, any value of \(x\) other than 3 will make the expression defined.