1/z-1/(2z)-1/(5z)=10/(z+1)

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Solution for 1/z-1/(2z)-1/(5z)=10/(z+1) equation: 


D( z )

5*z = 0

z+1 = 0

2*z = 0

z = 0

5*z = 0

5*z = 0

5*z = 0 // : 5

z = 0

z+1 = 0

z+1 = 0

z+1 = 0 // - 1

z = -1

2*z = 0

2*z = 0

2*z = 0 // : 2

z = 0

z = 0

z = 0

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

1/z-(1/(2*z))-(1/(5*z)) = 10/(z+1) // - 10/(z+1)

1/z-(10/(z+1))-(1/(2*z))-(1/(5*z)) = 0

1/z-10*(z+1)^-1+(-1/2)*z^-1+(-1/5)*z^-1 = 0

1/z-10/(z+1)-1/(2*z)-1/(5*z) = 0

(-10*2*5*z*z*z)/(2*5*z*z*z*(z+1))+(1*2*5*z*z*(z+1))/(2*5*z*z*z*(z+1))+(-1*5*z*z*(z+1))/(2*5*z*z*z*(z+1))+(-1*2*z*z*(z+1))/(2*5*z*z*z*(z+1)) = 0

1*2*5*z*z*(z+1)-1*5*z*z*(z+1)-1*2*z*z*(z+1)-10*2*5*z*z*z = 0

10*z^2-90*z^3-5*z^3-2*z^3-5*z^2-2*z^2 = 0

5*z^2-95*z^3-2*z^3-2*z^2 = 0

3*z^2-97*z^3 = 0

3*z^2-97*z^3 = 0

z^2*(3-97*z) = 0

3-97*z = 0 // - 3

-97*z = -3 // : -97

z = -3/(-97)

z = 3/97

z^2*(z-3/97) = 0

(z^2*(z-3/97))/(2*5*z*z*z*(z+1)) = 0

(z^2*(z-3/97))/(2*5*z*z*z*(z+1)) = 0 // * 2*5*z*z*z*(z+1)

z^2*(z-3/97) = 0

( z-3/97 )

z-3/97 = 0 // + 3/97

z = 3/97

( z^2 )

1*z^2 = 0 // : 1

z^2 = 0

z = 0

z in { 0} 

z = 3/97

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