It is known that 1 of m plus 1 of n equals 1 of M minus 1 of N, then n of M minus n of M equals 1 of n

It is known that 1 of m plus 1 of n equals 1 of M minus 1 of N, then n of M minus n of M equals 1 of n

1/m + 1/n = 1/(m-n)
That is, (M + n) / Mn = 1 / (m-n)
That is, (M + n) (m-n) / Mn = 1
n/m - m/n = (n^2-m^2)/mn = (m+n)(m-n)/mn = 1