x = 4
x / 3 = x + 4 / x + 2
Cross multiply
x * x + 2 = 3 * x + 4
Distribute
x^2 + 2x = 3x + 12
Set equal to zero
x^2 - x - 12 = 0
Factor
(x - 4)(x +3) = 0
Solve
x = 4 or x = -3
Length can’t be negative so x = 4
Check:
x / 3 = x + 4 / x + 2
4 / 3 = 4 + 4 / 4 + 2
4 / 3 = 8 / 6
4 / 3 = 4 / 3 :)