[x-(1/x)] / [1+(1/x)] = 3

[x-(1/x)] / [1+(1/x)] = 3

Multiply top and bottom of your fraction by x

so (x^2 - 1)/(x^2 + 1) = 3

cross-multiply
x^2 - 1 = 3x^2 + 3
x^2 = -2

no real solution
in complex numbers it would be
x = ±(√2)i