Question

how many values of x must be excluded in the expression \\(\frac{x - 2}{(x + 9)(x - 5)}\\)?
○ 0
○ 1
○ 2
○ 3

Explanation:

Step1: Identify excluded values rule

For a rational expression \(\frac{f(x)}{g(x)}\), values that make \(g(x) = 0\) are excluded (division by zero is undefined).

Step2: Solve \(g(x)=0\)

Given \(g(x)=(x + 9)(x - 5)\), set \((x + 9)(x - 5)=0\).
By zero - product property, if \(ab = 0\), then \(a = 0\) or \(b = 0\).
So, \(x+9 = 0\) or \(x - 5=0\).
For \(x + 9=0\), we get \(x=-9\).
For \(x - 5=0\), we get \(x = 5\).
There are 2 values (\(x=-9\) and \(x = 5\)) that make the denominator zero.

Answer:

2 (corresponding to the option with "2" as the value, e.g., if the option is "2" in the list, the answer is the option with text "2")