((8z+1)/(z-5))=-((3z)/(5-z))

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Solution for ((8z+1)/(z-5))=-((3z)/(5-z)) equation: 


D( z )

5-z = 0

z-5 = 0

5-z = 0

5-z = 0

5-z = 0 // - 5

-z = -5 // * -1

z = 5

z-5 = 0

z-5 = 0

z-5 = 0 // + 5

z = 5

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

(8*z+1)/(z-5) = -((3*z)/(5-z)) // + (3*z)/(5-z)

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

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

(8*z+1)*(5-z)+3*z*(z-5) = 0

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

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

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

DELTA = 24^2-(-5*4*5)

DELTA = 676

DELTA > 0

z = (676^(1/2)-24)/(-5*2) or z = (-676^(1/2)-24)/(-5*2)

z = -1/5 or z = 5

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

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

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

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

( z+1/5 )

z+1/5 = 0 // - 1/5

z = -1/5

( z-5 )

z-5 = 0 // + 5

z = 5

z in { 5} 

z = -1/5

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