4x/x-3+x/2=12/x-3

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Solution for 4x/x-3+x/2=12/x-3 equation: 


D( x )

x = 0

x = 0

x = 0

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

x/2+(4*x)/x-3 = 12/x-3 // - 12/x-3

x/2-(12/x)+(4*x)/x-3+3 = 0

x/2-12*x^-1+(4*x)/x-3+3 = 0

1/2*x^1-12*x^-1+4*x^0 = 0

(1/2*x^2+4*x^1-12*x^0)/(x^1) = 0 // * x^2

x^1*(1/2*x^2+4*x^1-12*x^0) = 0

x^1

(1/2)*x^2+4*x-12 = 0

(1/2)*x^2+4*x-12 = 0

DELTA = 4^2-(-12*4*(1/2))

DELTA = 40

DELTA > 0

x = (40^(1/2)-4)/(2*(1/2)) or x = (-40^(1/2)-4)/(2*(1/2))

x = 2*10^(1/2)-4 or x = -2*10^(1/2)-4

x in { -2*10^(1/2)-4, 2*10^(1/2)-4} 

x in { -2*10^(1/2)-4, 2*10^(1/2)-4 }

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