((2/5)+3x)/(4x-(3/x))

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Solution for ((2/5)+3x)/(4x-(3/x)) equation: 


D( x )

x = 0

4*x-(3/x) = 0

x = 0

x = 0

4*x-(3/x) = 0

4*x-(3/x) = 0

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

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

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

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

x^1

4*x^2-3 = 0

4*x^2-3 = 0

DELTA = 0^2-(-3*4*4)

DELTA = 48

DELTA > 0

x = (48^(1/2)+0)/(2*4) or x = (0-48^(1/2))/(2*4)

x = (3^(1/2))/2 or x = (-3^(1/2))/2

x in { (-3^(1/2))/2, (3^(1/2))/2} 

x in (-oo:(-3^(1/2))/2) U ((-3^(1/2))/2:0) U (0:(3^(1/2))/2) U ((3^(1/2))/2:+oo)

(3*x+2/5)/(4*x-(3/x)) = 0

(3*x+2/5)/(4*x-3*x^-1) = 0

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

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

4*x^2 = 3 // : 4

x^2 = 3/4

x^2 = 3/4 // ^ 1/2

abs(x) = (3/4)^(1/2)

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

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

(3*x+2/5)/(x^-1*(x-(3/4)^(1/2))*(x+(3/4)^(1/2))) = 0

3*x+2/5 = 0 // - 2/5

3*x = -2/5 // : 3

x = -2/5/3

x = -2/15

x = -2/15

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