SOLUTION: i need help with this (1/x)+(1/x+2)=(1/3) to this 2+sqrt10 and 2-sqrt10 thanks for your time and help

Question 990944: i need help with this (1/x)+(1/x+2)=(1/3)

to this 2+sqrt10 and 2-sqrt10
thanks for your time and help
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
(1/x) + (1/x+2) = (1/3)
(x+2+x) / (x*(x+2)) = (1/3)
(2x+2) / (x^2+2x) = (1/3)
cross multiply the fractions
3*(2x+2) = x^2 + 2x
6x+6 = x^2 + 2x
x^2 - 4x - 6 = 0
use quadratic equation
x = (4 + square root(16-4*(-6))) / 2 = (4+2sqrt(10))/2 = 2+sqrt(10)
x = (4 - square root(16-4*(-6))) / 2 = (4-2sqrt(10))/2 = 2-sqrt(10)

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