(5z)/(z-5)-2/(z-1)=3

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Solution for (5z)/(z-5)-2/(z-1)=3 equation: 


D( z )

z-1 = 0

z-5 = 0

z-1 = 0

z-1 = 0

z-1 = 0 // + 1

z = 1

z-5 = 0

z-5 = 0

z-5 = 0 // + 5

z = 5

z in (-oo:1) U (1:5) U (5:+oo)

(5*z)/(z-5)-(2/(z-1)) = 3 // - 3

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

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

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

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

5*z*(z-1)-2*(z-5)-3*(z-5)*(z-1) = 0

5*z^2-3*z^2-7*z+18*z-15+10 = 0

2*z^2+11*z-5 = 0

2*z^2+11*z-5 = 0

2*z^2+11*z-5 = 0

DELTA = 11^2-(-5*2*4)

DELTA = 161

DELTA > 0

z = (161^(1/2)-11)/(2*2) or z = (-161^(1/2)-11)/(2*2)

z = (161^(1/2)-11)/4 or z = (-(161^(1/2)+11))/4

(z+(161^(1/2)+11)/4)*(z-((161^(1/2)-11)/4)) = 0

((z+(161^(1/2)+11)/4)*(z-((161^(1/2)-11)/4)))/((z-5)*(z-1)) = 0

((z+(161^(1/2)+11)/4)*(z-((161^(1/2)-11)/4)))/((z-5)*(z-1)) = 0 // * (z-5)*(z-1)

(z+(161^(1/2)+11)/4)*(z-((161^(1/2)-11)/4)) = 0

( z+(161^(1/2)+11)/4 )

z+(161^(1/2)+11)/4 = 0 // - (161^(1/2)+11)/4

z = -((161^(1/2)+11)/4)

( z-((161^(1/2)-11)/4) )

z-((161^(1/2)-11)/4) = 0 // + (161^(1/2)-11)/4

z = (161^(1/2)-11)/4

z in { -((161^(1/2)+11)/4), (161^(1/2)-11)/4 }

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