abs((3z-1)/(z-3))=1

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Solution for abs((3z-1)/(z-3))=1 equation: 


D( z )

z-3 = 0

z-3 = 0

z-3 = 0

z-3 = 0 // + 3

z = 3

z in (-oo:3) U (3:+oo)

abs((3*z-1)/(z-3)) = 1 // - 1

abs((3*z-1)/(z-3))-1 = 0

abs((3*z-1)/(z-3))-1 = 0

z in (-oo:+oo)

abs((3*z-1)/(z-3))

(3*z-1)/(z-3) >= 0

( 3*z-1 )

3*z-1 >= 0 // + 1

3*z >= 1 // : 3

z >= 1/3

( z-3 )

z-3 >= 0 // + 3

z >= 3

(-oo:1/3)(1/3:3)(3:+oo)3*z-1-++z-3--+

z in (-oo:1/3> U <3:+oo)

(3*z-1)/(z-3)-1 = 0

z in (1/3:3)

-((3*z-1)/(z-3))-1 = 0

abs((3*z-1)/(z-3))-1 = 0

/| (3*z-1)/(z-3)-1 = 0 i z in (-oo:1/3> U <3:+oo)| -((3*z-1)/(z-3))-1 = 0 i z in (1/3:3)

z in (-oo:1/3> U <3:+oo)

(3*z-1)/(z-3)-1 = 0

(3*z-1)/(z-3)+(-1*(z-3))/(z-3) = 0

3*z-1*(z-3)-1 = 0

2*z+2 = 0

(2*z+2)/(z-3) = 0

(2*z+2)/(z-3) = 0 // * z-3

2*z+2 = 0

2*z+2 = 0 // - 2

2*z = -2 // : 2

z = -2/2

z = -1

z in (1/3:3)

-((3*z-1)/(z-3))-1 = 0

(-1*(3*z-1))/(z-3)-1 = 0

(-1*(3*z-1))/(z-3)+(-1*(z-3))/(z-3) = 0

-1*(3*z-1)-1*(z-3) = 0

4-4*z = 0

(4-4*z)/(z-3) = 0

(4-4*z)/(z-3) = 0 // * z-3

4-4*z = 0

4-4*z = 0 // - 4

-4*z = -4 // : -4

z = -4/(-4)

z = 1

z in { -1, 1 }

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