(z/(z-5))-(4/(z-8))

Solution for (z/(z-5))-(4/(z-8)) equation:

D( z )

z-8 = 0

z-5 = 0

z-8 = 0

z-8 = 0

z-8 = 0 // + 8

z = 8

z-5 = 0

z-5 = 0

z-5 = 0 // + 5

z = 5

z in (-oo:5) U (5:8) U (8:+oo)

z/(z-5)-(4/(z-8)) = 0

z/(z-5)-4*(z-8)^-1 = 0

z/(z-5)-4/(z-8) = 0

(z*(z-8))/((z-5)*(z-8))+(-4*(z-5))/((z-5)*(z-8)) = 0

z*(z-8)-4*(z-5) = 0

z^2-12*z+20 = 0

z^2-12*z+20 = 0

z^2-12*z+20 = 0

DELTA = (-12)^2-(1*4*20)

DELTA = 64

DELTA > 0

z = (64^(1/2)+12)/(1*2) or z = (12-64^(1/2))/(1*2)

z = 10 or z = 2

(z-2)*(z-10) = 0

((z-2)*(z-10))/((z-5)*(z-8)) = 0

((z-2)*(z-10))/((z-5)*(z-8)) = 0 // * (z-5)*(z-8)

(z-2)*(z-10) = 0

( z-10 )

z-10 = 0 // + 10

z = 10

( z-2 )

z-2 = 0 // + 2

z = 2

z in { 10, 2 }