(6/(z-7))-(4/(z-5))-(2z/(z-7))

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Solution for (6/(z-7))-(4/(z-5))-(2z/(z-7)) equation: 


D( z )

z-7 = 0

z-5 = 0

z-7 = 0

z-7 = 0

z-7 = 0 // + 7

z = 7

z-5 = 0

z-5 = 0

z-5 = 0 // + 5

z = 5

z in (-oo:5) U (5:7) U (7:+oo)

6/(z-7)-(4/(z-5))-((2*z)/(z-7)) = 0

6/(z-7)-4*(z-5)^-1-2*z*(z-7)^-1 = 0

6/(z-7)-4/(z-5)+(-2*z)/(z-7) = 0

(6*(z-5))/((z-7)*(z-5))+(-4*(z-7))/((z-7)*(z-5))+(-2*z*(z-5))/((z-7)*(z-5)) = 0

6*(z-5)-4*(z-7)-2*z*(z-5) = 0

2*z-2*z^2+10*z-2 = 0

12*z-2*z^2-2 = 0

12*z-2*z^2-2 = 0

2*(6*z-z^2-1) = 0

6*z-z^2-1 = 0

DELTA = 6^2-(-1*(-1)*4)

DELTA = 32

DELTA > 0

z = (32^(1/2)-6)/(-1*2) or z = (-32^(1/2)-6)/(-1*2)

z = (4*2^(1/2)-6)/(-2) or z = (-4*2^(1/2)-6)/(-2)

2*(z-((4*2^(1/2)-6)/(-2)))*(z-((-4*2^(1/2)-6)/(-2))) = 0

(2*(z-((4*2^(1/2)-6)/(-2)))*(z-((-4*2^(1/2)-6)/(-2))))/((z-7)*(z-5)) = 0

(2*(z-((4*2^(1/2)-6)/(-2)))*(z-((-4*2^(1/2)-6)/(-2))))/((z-7)*(z-5)) = 0 // * (z-7)*(z-5)

2*(z-((4*2^(1/2)-6)/(-2)))*(z-((-4*2^(1/2)-6)/(-2))) = 0

( 2 )

2 = 0

z belongs to the empty set

( z-((-4*2^(1/2)-6)/(-2)) )

z-((-4*2^(1/2)-6)/(-2)) = 0 // + (-4*2^(1/2)-6)/(-2)

z = (-4*2^(1/2)-6)/(-2)

( z-((4*2^(1/2)-6)/(-2)) )

z-((4*2^(1/2)-6)/(-2)) = 0 // + (4*2^(1/2)-6)/(-2)

z = (4*2^(1/2)-6)/(-2)

z in { (-4*2^(1/2)-6)/(-2), (4*2^(1/2)-6)/(-2) }

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