1/z-1/(4z)-1/(3z)=12/(z+1)

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Solution for 1/z-1/(4z)-1/(3z)=12/(z+1) equation:


D( z )

4*z = 0

z+1 = 0

3*z = 0

z = 0

4*z = 0

4*z = 0

4*z = 0 // : 4

z = 0

z+1 = 0

z+1 = 0

z+1 = 0 // - 1

z = -1

3*z = 0

3*z = 0

3*z = 0 // : 3

z = 0

z = 0

z = 0

z in (-oo:-1) U (-1:0) U (0:+oo)

1/z-(1/(4*z))-(1/(3*z)) = 12/(z+1) // - 12/(z+1)

1/z-(12/(z+1))-(1/(4*z))-(1/(3*z)) = 0

1/z-12*(z+1)^-1+(-1/4)*z^-1+(-1/3)*z^-1 = 0

1/z-12/(z+1)-1/(4*z)-1/(3*z) = 0

(-12*3*4*z*z*z)/(3*4*z*z*z*(z+1))+(1*3*4*z*z*(z+1))/(3*4*z*z*z*(z+1))+(-1*3*z*z*(z+1))/(3*4*z*z*z*(z+1))+(-1*4*z*z*(z+1))/(3*4*z*z*z*(z+1)) = 0

1*3*4*z*z*(z+1)-1*3*z*z*(z+1)-1*4*z*z*(z+1)-12*3*4*z*z*z = 0

12*z^2-132*z^3-3*z^3-4*z^3-3*z^2-4*z^2 = 0

9*z^2-135*z^3-4*z^3-4*z^2 = 0

5*z^2-139*z^3 = 0

5*z^2-139*z^3 = 0

z^2*(5-139*z) = 0

5-139*z = 0 // - 5

-139*z = -5 // : -139

z = -5/(-139)

z = 5/139

z^2*(z-5/139) = 0

(z^2*(z-5/139))/(3*4*z*z*z*(z+1)) = 0

(z^2*(z-5/139))/(3*4*z*z*z*(z+1)) = 0 // * 3*4*z*z*z*(z+1)

z^2*(z-5/139) = 0

( z-5/139 )

z-5/139 = 0 // + 5/139

z = 5/139

( z^2 )

1*z^2 = 0 // : 1

z^2 = 0

z = 0

z in { 0}

z = 5/139

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