NMTC 2002 Kaprekar Contest

Let \(a*b\space =\space a+b+ab\). For example,

\(6*2\space =\space 6+2+(6\times2)\space =\space 20\)

If \(a*x\space =\space 0\), then \(x\) is

(A) \(\dfrac{a}{a+1}\)

(B) \(\dfrac{a}{a-1}\)

(C) \(\dfrac{-a}{a-1}\)

(D) \(\dfrac{-a}{a+1}\)

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