Determine the value or values of the variable where the expression is defined.
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A) all real numbers except x = 0
B) all real numbers except x = 3, x = 6
C) all real numbers except x = 5
D) all real numbers except x = -3, x = -6

Question

Determine the value or values of the variable where the expression is defined.
-
A) all real numbers except x = 0 
B) all real numbers except x = 3, x = 6 
C) all real numbers except x = 5 
D) all real numbers except x = -3, x = -6

Quizplus · Accepted Answer

The expression involves division by x-3 and x-6, which cannot be zero. Therefore, x cannot be equal to 3 or 6. All other real numbers are valid choices for x. The given expression is undefined when the denominator is equal to zero. So,
x + 3 = 0  or x - 6 = 0
x = -3 or x = 6

Therefore, the expression is undefined at x = -3 and x = 6. For all other real numbers, the expression is defined. Hence, the answer is B, all real numbers except x = 3, x = 6.

Determine the Value or Values of the Variable Where the Expression