If abc ≠ 1 and the sum of the reciprocals of a, b, and c equals the reciprocal of the product of a, b, and c, then a =  Options.
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)
Answer is (1 + b + c)/(bc) though it took me around 4 minutes to get that.
<result>C</result>
If abc ≠ 1 and the sum of the reciprocals of a, b, and c equals the reciprocal of the product of a, b, and c, then a =