If abc ≠ 0 and the sum of the reciprocals of a, b, and c equals the reciprocal of the product of a, b, and c, then a =
A. (1 + bc)/(b + c)
B. (1 – bc)/(b + c)
C. (1 + b + c)/(bc)
D. (1 – b – c)/(bc)
E. (1 – b – c)/(b + c)
OA B
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If abc 0 and the sum of the reciprocals of a, b, and c equals the reciprocal of the product of a, b, and c, then a =
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BTGmoderatorDC
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Solution:BTGmoderatorDC wrote: ↑Wed Aug 12, 2020 6:24 pmIf abc ≠ 0 and the sum of the reciprocals of a, b, and c equals the reciprocal of the product of a, b, and c, then a =
A. (1 + bc)/(b + c)
B. (1 – bc)/(b + c)
C. (1 + b + c)/(bc)
D. (1 – b – c)/(bc)
E. (1 – b – c)/(b + c)
OA B
We are given that 1/a + 1/b + 1/c = 1/abc and we need to solve a in terms of b and c. Multiplying the equation by abc, we have:
bc + ac + ab = 1
a(c + b) = 1 - bc
a = (1 - bc)/(b + c)
Answer: B
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