If \(abc \ne 0\) 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. \(\dfrac{1 + bc}{b + c}\)
B. \(\dfrac{1 - bc}{b + c}\)
C. \(\dfrac{1 + b + c}{bc}\)
D. \(\dfrac{1 - b - c}{bc}\)
E. \(\dfrac{1 - b - c}{b + c}\)
Answer: B
Source: Manhattan GMAT
If \(abc \ne 0\) and the sum of the reciprocals of \(a, b,\) and \(c\) equals the reciprocal of the product of \(a, b,\)
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Solution:M7MBA wrote: ↑Thu Oct 29, 2020 1:05 pmIf \(abc \ne 0\) 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. \(\dfrac{1 + bc}{b + c}\)
B. \(\dfrac{1 - bc}{b + c}\)
C. \(\dfrac{1 + b + c}{bc}\)
D. \(\dfrac{1 - b - c}{bc}\)
E. \(\dfrac{1 - b - c}{b + c}\)
Answer: 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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