I assume we need to find the number that satisfies the conditions from the problem.

let n is the number we need to find and x is any number

1/(nx) = 2 + n multiply both sides by nx

n^2x + 2nx - 1 = 0

x(n^2 + 2n) = 1

this equation needs to be satisfied for any x. Since this is not true for example for x = 0 (0 = 1) follows the equation has no solution. There is no such number n.