(1/2)*((x/3)-(5/6))=(1/3)*((1/(2x))-2)+(1/4)

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Solution for (1/2)*((x/3)-(5/6))=(1/3)*((1/(2x))-2)+(1/4) equation: 


D( x )

2*x = 0

2*x = 0

2*x = 0

2*x = 0 // : 2

x = 0

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

(1/2)*(x/3-(5/6)) = (1/3)*(1/(2*x)-2)+1/4 // - (1/3)*(1/(2*x)-2)+1/4

(1/2)*(x/3-(5/6))-((1/3)*(1/(2*x)-2))-(1/4) = 0

(1/2)*(x/3-5/6)+(-1/3)*(1/(2*x)-2)-1/4 = 0

1/2*(1/3*x-5/6)-1/3*(1/2*x^-1-2)-1/4 = 0

(1/2*4*(1/3*x-5/6))/4+(-1/3*4*(1/2*x^-1-2))/4-1/4 = 0

1/2*4*(1/3*x-5/6)-1/3*4*(1/2*x^-1-2)-1 = 0

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

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

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

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

1*x^2 = 1 // : 1

x^2 = 1

x^2 = 1 // ^ 1/2

abs(x) = 1

x = 1 or x = -1

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

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

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

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

( 2/3*x^-1 )

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

x^-1 = 0

x naleu017Cy do O

( x+1 )

x+1 = 0 // - 1

x = -1

( x-1 )

x-1 = 0 // + 1

x = 1

x in { -1, 1 }

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