4/2x-6=2/x-3

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Solution for 4/2x-6=2/x-3 equation: 


D( x )

x = 0

x = 0

x = 0

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

(4/2)*x-6 = 2/x-3 // - 2/x-3

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

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

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

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

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

x^1

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

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

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

DELTA = 25

DELTA > 0

x = (25^(1/2)+3)/(2*2) or x = (3-25^(1/2))/(2*2)

x = 2 or x = -1/2

x in { -1/2, 2} 

x in { -1/2, 2 }

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