If m and n are nonzero and such that mn+n = m , which of the

fskilnik wrote:If m and n are nonzero and such that mn+n = m , which of the following is equal to the difference between the reciprocal of m and the reciprocal of n (in that order)?

(A) the opposite of mn
(B) the reciprocal of mn
(C) the opposite of 1
(D) the reciprocal of 1
(E) none above

\[m,n\,\, \ne 0\]
\[mn + n = m\]
\[? = \frac{1}{m} - \frac{1}{n} = \frac{n}{{mn}} - \frac{m}{{nm}} = \frac{{n - m}}{{nm}}\,\,\mathop = \limits^{\left( * \right)} \,\,\frac{{ - mn}}{{nm}} = - 1\]
\[\left( * \right)\,\,\,mn + n = m\,\,\,\,\, \Rightarrow \,\,\,n - m = - mn\]
The right answer is therefore (C), because -1 is the opposite of 1.


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.