x =±sqrt(1/3)
step-by-step explanation:
x+4/6x=1/x
multiply each side by 6x to get rid of the fractions
6x*(x+4/6x)=1/x*6x
distribute
6x^2 +4 = 6
subtract 4 from each side
6x^2 +4-4 = 6-4
6x^2 =2
divide by 6
6x^2/6 = 2/6
x^2 = 1/3
take the square root of each side
sqrt(x^2) = ±sqrt(1/3)
x =±sqrt(1/3)