Answer:

x+(1/x) = 4(x-(1/x)

The rest is just algebra.

x+(1/x) = 4(x-(1/x)

x + 1/x = 4 - 4/x

x + 5/x - 4 = 0

Multiplying both sides, we have:

x^2 - 4x + 5. = 0

Factoring:

(x+1) (x-5) = 0