(1/(3x)-1/(6x^2))/(1-1/(2x))

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Solution for (1/(3x)-1/(6x^2))/(1-1/(2x)) equation:


D( x )

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

3*x = 0

6*x^2 = 0

2*x = 0

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

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

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

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

x^-1 = 2

-1 < 0

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

1 = 2*x^1 // : 2

1/2 = x^1

x = 1/2

3*x = 0

3*x = 0

3*x = 0 // : 3

x = 0

6*x^2 = 0

6*x^2 = 0

6*x^2 = 0 // : 6

x^2 = 0

x = 0

2*x = 0

2*x = 0

2*x = 0 // : 2

x = 0

x in (-oo:0) U (0:1/2) U (1/2:+oo)

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

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

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

1/3*x^-1-1/6*x^-2 = 0

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

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

x^-1 = 2

-1 < 0

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

1 = 2*x^1 // : 2

1/2 = x^1

x = 1/2

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

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

( 1/3*x^-1 )

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

x^-1 = 0

x należy do O

( x-1/2 )

x-1/2 = 0 // + 1/2

x = 1/2

x in { 1/2}

x belongs to the empty set

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