x-3/((x/4)-(4/x))

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


D( x )

x = 0

x/4-(4/x) = 0

x = 0

x = 0

x/4-(4/x) = 0

x/4-(4/x) = 0

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

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

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

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

x^1

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

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

DELTA = 0^2-(-4*4*(1/4))

DELTA = 4

DELTA > 0

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

x = 4 or x = -4

x in { -4, 4} 

x in (-oo:-4) U (-4:0) U (0:4) U (4:+oo)

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

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

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

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

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

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

1/4*x^2 = 4 // : 1/4

x^2 = 16

x^2 = 16 // ^ 1/2

abs(x) = 4

x = 4 or x = -4

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

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

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

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

x^2-19 = 0

(x^2-19)/(x^-1*(x-4)*(x+4)) = 0

(x^2-19)/(x^-1*(x-4)*(x+4)) = 0 // * x^-1*(x-4)*(x+4)

x^2-19 = 0

1*x^2 = 19 // : 1

x^2 = 19

x^2 = 19 // ^ 1/2

abs(x) = 19^(1/2)

x = 19^(1/2) or x = -19^(1/2)

x in { 19^(1/2), -19^(1/2) }

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