4/2x-5=3/x-2

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Solution for 4/2x-5=3/x-2 equation: 


D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

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

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

x^1

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

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

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

DELTA = 33

DELTA > 0

x = (33^(1/2)+3)/(2*2) or x = (3-33^(1/2))/(2*2)

x = (33^(1/2)+3)/4 or x = (3-33^(1/2))/4

x in { (3-33^(1/2))/4, (33^(1/2)+3)/4} 

x in { (3-33^(1/2))/4, (33^(1/2)+3)/4 }

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