x=(1/(3x-4))

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Solution for x=(1/(3x-4)) equation:


D( x )

3*x-4 = 0

3*x-4 = 0

3*x-4 = 0

3*x-4 = 0 // + 4

3*x = 4 // : 3

x = 4/3

x in (-oo:4/3) U (4/3:+oo)

x = 1/(3*x-4) // - 1/(3*x-4)

x-(1/(3*x-4)) = 0

x-(3*x-4)^-1 = 0

x-1/(3*x-4) = 0

(x*(3*x-4))/(3*x-4)-1/(3*x-4) = 0

x*(3*x-4)-1 = 0

3*x^2-4*x-1 = 0

3*x^2-4*x-1 = 0

3*x^2-4*x-1 = 0

DELTA = (-4)^2-(-1*3*4)

DELTA = 28

DELTA > 0

x = (28^(1/2)+4)/(2*3) or x = (4-28^(1/2))/(2*3)

x = (2*7^(1/2)+4)/6 or x = (4-2*7^(1/2))/6

(x-((4-2*7^(1/2))/6))*(x-((2*7^(1/2)+4)/6)) = 0

((x-((4-2*7^(1/2))/6))*(x-((2*7^(1/2)+4)/6)))/(3*x-4) = 0

((x-((4-2*7^(1/2))/6))*(x-((2*7^(1/2)+4)/6)))/(3*x-4) = 0 // * 3*x-4

(x-((4-2*7^(1/2))/6))*(x-((2*7^(1/2)+4)/6)) = 0

( x-((2*7^(1/2)+4)/6) )

x-((2*7^(1/2)+4)/6) = 0 // + (2*7^(1/2)+4)/6

x = (2*7^(1/2)+4)/6

( x-((4-2*7^(1/2))/6) )

x-((4-2*7^(1/2))/6) = 0 // + (4-2*7^(1/2))/6

x = (4-2*7^(1/2))/6

x in { (2*7^(1/2)+4)/6, (4-2*7^(1/2))/6 }

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