Question

question 34 of 42
which of the following values of x makes the rational
\\(\frac{x + 9}{3 - x}\\)
a. 3
b. -9
c. 9
d. -3

Explanation:

Step1: Recall when a rational expression is undefined

A rational expression \(\frac{f(x)}{g(x)}\) is undefined when the denominator \(g(x) = 0\). So we need to find the value of \(x\) that makes the denominator \(3 - x = 0\).

Step2: Solve the equation for the denominator

Set \(3 - x = 0\). To solve for \(x\), we can add \(x\) to both sides: \(3 = x\), or \(x = 3\). So when \(x = 3\), the denominator is zero, and the rational expression \(\frac{x + 9}{3 - x}\) is undefined.

Answer:

A. 3 (assuming option A is 3, as per the context of the problem where we found \(x = 3\) makes the expression undefined)