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)
OA [/img]A
Can someone explain how to solve this?
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bryan22583
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I suspect that the question stem and the OA should read as I've posted them here.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)
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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We can simplify the eq. [ (2b)¯¹ - (2¯¹)b ] / (b¯¹ + 1¯¹)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)
[1/2b-b/2]/[1/b+1]
[(1-b^2)b/2b]/(1+b)]
[(1+b)(1-b)/2(1+b)]
(1-b)/2 ... (A)
