If \(abc \ne 0\) and the sum of the reciprocals of \(a, b,\) and \(c\) equals the reciprocal of the product of \(a, b,\)

[M7MBA]

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

[Scott@TargetTestPrep]

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

Solution:

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