(7z/(7z-1))-(1/(1-7z))

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Solution for (7z/(7z-1))-(1/(1-7z)) equation: 


D( z )

7*z-1 = 0

1-(7*z) = 0

7*z-1 = 0

7*z-1 = 0

7*z-1 = 0 // + 1

7*z = 1 // : 7

z = 1/7

1-(7*z) = 0

1-(7*z) = 0

1-7*z = 0

1-7*z = 0 // - 1

-7*z = -1 // : -7

z = -1/(-7)

z = 1/7

z in (-oo:1/7) U (1/7:+oo)

(7*z)/(7*z-1)-(1/(1-(7*z))) = 0

(7*z)/(7*z-1)-(1-7*z)^-1 = 0

(7*z)/(7*z-1)-1/(1-7*z) = 0

(7*z*(1-7*z))/((7*z-1)*(1-7*z))+(-1*(7*z-1))/((7*z-1)*(1-7*z)) = 0

7*z*(1-7*z)-1*(7*z-1) = 0

1-49*z^2 = 0

(1-49*z^2)/((7*z-1)*(1-7*z)) = 0

(1-49*z^2)/((7*z-1)*(1-7*z)) = 0 // * (7*z-1)*(1-7*z)

1-49*z^2 = 0

-49*z^2 = -1 // : -49

z^2 = 1/49

z^2 = 1/49 // ^ 1/2

abs(z) = 1/7

z = 1/7 or z = -1/7

z in { 1/7} 

z = -1/7

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