((ab)² + 3ab - 18) / (a-1)(a+2) = 0
Which of the following could be the value of b?
I: 1
II: 2
III: 3
A) I
B) II
C) I and II
D) I and III
E) I, II and III
The numerator must be equal to 0.
The denominator cannot be equal to 0, requiring that a≠1 and a≠-2.
(ab)² + 3ab - 18 = 0
(ab + 6)(ab - 3) = 0
ab = -6 or ab = 3.
I: b=1
If ab = -6, then a = -6.
This works.
Eliminate B, which does not include I.
II: b=2.
If ab = -6, then a = -3.
This works.
Eliminate A and D, which do not include II.
III: b=3
If ab = -6, then a = -2.
Not possible, since a≠-2.
If ab = 3, then a=1.
Not possible, since a≠1.
Eliminate E, which includes III.
The correct answer is
C.
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