bryan22583 wrote:Which of the following is equivalent to [ (2b)¯¹ - (2¯¹)b ] / (b¯¹ + 1¯¹)?
A) (1-b)/2
B) (b-1)/2
C) (b^2)-1/2b
D) (1-b^2)/2b
E) 2b/(1-b^2)
I suspect that the question stem and the OA should read as I've posted them here.
Remember that a negative exponent means RECIPROCAL:
x¯¹ = 1/x.
Plug b=3 into the given expression:
[ (2b)¯¹ - (2¯¹)b ] / (b¯¹ + 1¯¹)
= [ (2*3)¯¹ - (2¯¹)3 ] / (3¯¹ + 1¯¹)
= (1/6 - 3/2) / (1/3 + 1)
= (-8/6) / (4/3)
= (-4/3) * (3/4)
= -1. This is our target
Now plug b=3 into the answer choices to see which yields our target of -1.
Answer choice
A:
(1-b)/2 = (1-3)/2 = -2/2 = -1.
The correct answer is
A.
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