1/3(4x-5)-1/x=3/2x-2

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Solution for 1/3(4x-5)-1/x=3/2x-2 equation: 


D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

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

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

4*x-1/3*x^2-10/3*x-2 = 0

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

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

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

DELTA = (2/3)^2-(-2*(-1/3)*4)

DELTA = -20/9

DELTA < 0

1 = 0

1/(2*x) = 0

1/(2*x) = 0 // * 2*x

1 = 0

x belongs to the empty set

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