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555-605 (Medium)|   Algebra|   Exponents|      
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mborski
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Which of the following is equivalent to (2b)^-1 - 2^-1b/b^-1 + 1^-1 ? Updated on: 20 Jan 2020, 23:00
Originally posted by mborski on 20 Jan 2020, 18:00.
Last edited by Bunuel on 20 Jan 2020, 23:00, edited 1 time in total.
Renamed the topic and edited the question.
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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35% (medium)

Question Stats:

67% (01:45) correct 33% (02:32) wrong based on 228 sessions

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Which of the following is equivalent to \(\frac{(2b)^{-1} - 2^{-1}b}{b^{-1} + 1^{-1}}\) ?


A. \(\frac{1 - b}{2}\)

B. \(\frac{b - 1}{2}\)

C. \(\frac{b^2 - 1}{2b}\)

D. \(\frac{1 - b^2}{2b}\)

E. \(\frac{2b}{1 - b^2}\)


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A
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Which of the following is equivalent to (2b)^-1 - 2^-1b/b^-1 + 1^-1 ? 20 Jan 2020, 18:10
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Option A
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Which of the following is equivalent to (2b)^-1 - 2^-1b/b^-1 + 1^-1 ? 21 Jan 2020, 09:43
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Solution



To find
We need to determine
    • The value of the given expression

Approach and Working out
Numerator of the given expression = \((2b)^{-1} – 2^{-1} b = \frac{1}{2b} – \frac{b}{2} = \frac{(1}{b – b)/2} = \frac{(1 – b^2)}{2b}\)
Denominator of the given expression = \(b^{-1} + 1^{-1} = \frac{1}{b} + 1 = \frac{(1 + b)}{b}\)
    • Hence, the value of the expression = \(\frac{(1 – b^2)}{2b} * \frac{b}{(1 + b)} = \frac{(1 – b)}{2}\)

Thus, option A is the correct answer.

Correct Answer: Option A
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Which of the following is equivalent to (2b)^-1 - 2^-1b/b^-1 + 1^-1 ? 21 Jan 2020, 09:48
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Alternate Solution



To find
We need to determine
    • The value of the given expression

Approach and Working out
Assuming b = 2, the value of the expression = -0.5

Assuming the same value of b, the value of the options:
    A. -0.5
    B. 0.5
    C. 0.75
    D. -0.75
    E. 1.33

Thus, option A is the correct answer.

Correct Answer: Option A
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Which of the following is equivalent to (2b)^-1 - 2^-1b/b^-1 + 1^-1 ? 17 May 2022, 22:56
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EgmatQuantExpert

Alternate Solution



To find
We need to determine
    • The value of the given expression

Approach and Working out
Assuming b = 2, the value of the expression = -0.5

Assuming the same value of b, the value of the options:
    A. -0.5
    B. 0.5
    C. 0.75
    D. -0.75
    E. 1.33

Thus, option A is the correct answer.

Correct Answer: Option A
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This is incorrect unfortunately. If you plug in 2, you end up with (-0.75/1.25) = -0.6 which doesn't match up with any of the answer choices. The only way to do this is algebraically I think. Unless you can show how plugging in 2 gives that result.
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Which of the following is equivalent to (2b)^-1 - 2^-1b/b^-1 + 1^-1 ? 15 Oct 2023, 19:59
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