3/(z^2-8z+7)-1/(z-7)=1/(7z-7)

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Solution for 3/(z^2-8z+7)-1/(z-7)=1/(7z-7) equation: 


D( z )

7*z-7 = 0

z-7 = 0

z^2-(8*z)+7 = 0

7*z-7 = 0

7*z-7 = 0

7*z-7 = 0 // + 7

7*z = 7 // : 7

z = 7/7

z = 1

z-7 = 0

z-7 = 0

z-7 = 0 // + 7

z = 7

z^2-(8*z)+7 = 0

z^2-(8*z)+7 = 0

z^2-8*z+7 = 0

z^2-8*z+7 = 0

DELTA = (-8)^2-(1*4*7)

DELTA = 36

DELTA > 0

z = (36^(1/2)+8)/(1*2) or z = (8-36^(1/2))/(1*2)

z = 7 or z = 1

z in (-oo:1) U (1:7) U (7:+oo)

3/(z^2-(8*z)+7)-(1/(z-7)) = 1/(7*z-7) // - 1/(7*z-7)

3/(z^2-(8*z)+7)-(1/(z-7))-(1/(7*z-7)) = 0

3/(z^2-8*z+7)-(z-7)^-1-(7*z-7)^-1 = 0

3/(z^2-8*z+7)-1/(z-7)-1/(7*z-7) = 0

z^2-8*z+7 = 0

z^2-8*z+7 = 0

z^2-8*z+7 = 0

DELTA = (-8)^2-(1*4*7)

DELTA = 36

DELTA > 0

z = (36^(1/2)+8)/(1*2) or z = (8-36^(1/2))/(1*2)

z = 7 or z = 1

(z-1)*(z-7) = 0

3/((z-1)*(z-7))-1/(z-7)-1/(7*z-7) = 0

(3*(7*z-7))/((z-1)*(z-7)*(7*z-7))+(-1*(z-1)*(7*z-7))/((z-1)*(z-7)*(7*z-7))+(-1*(z-1)*(z-7))/((z-1)*(z-7)*(7*z-7)) = 0

3*(7*z-7)-1*(z-1)*(7*z-7)-1*(z-1)*(z-7) = 0

35*z-7*z^2-z^2+8*z-28-7 = 0

43*z-8*z^2-35 = 0

43*z-8*z^2-35 = 0

43*z-8*z^2-35 = 0

DELTA = 43^2-(-35*(-8)*4)

DELTA = 729

DELTA > 0

z = (729^(1/2)-43)/(-8*2) or z = (-729^(1/2)-43)/(-8*2)

z = 1 or z = 35/8

(z-1)*(z-35/8) = 0

((z-1)*(z-35/8))/((z-1)*(z-7)*(7*z-7)) = 0

((z-1)*(z-35/8))/((z-1)*(z-7)*(7*z-7)) = 0 // * (z-1)*(z-7)*(7*z-7)

(z-1)*(z-35/8) = 0

( z-1 )

z-1 = 0 // + 1

z = 1

( z-35/8 )

z-35/8 = 0 // + 35/8

z = 35/8

z in { 1} 

z = 35/8

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