1/(z+2)+3/(z+4)=2/(z^2+6z+8)

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Solution for 1/(z+2)+3/(z+4)=2/(z^2+6z+8) equation: 


D( z )

z+4 = 0

z^2+6*z+8 = 0

z+2 = 0

z+4 = 0

z+4 = 0

z+4 = 0 // - 4

z = -4

z^2+6*z+8 = 0

z^2+6*z+8 = 0

z^2+6*z+8 = 0

DELTA = 6^2-(1*4*8)

DELTA = 4

DELTA > 0

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

z = -2 or z = -4

z+2 = 0

z+2 = 0

z+2 = 0 // - 2

z = -2

z in (-oo:-4) U (-4:-2) U (-2:+oo)

1/(z+2)+3/(z+4) = 2/(z^2+6*z+8) // - 2/(z^2+6*z+8)

1/(z+2)+3/(z+4)-(2/(z^2+6*z+8)) = 0

1/(z+2)+3/(z+4)-2*(z^2+6*z+8)^-1 = 0

1/(z+2)+3/(z+4)-2/(z^2+6*z+8) = 0

z^2+6*z+8 = 0

z^2+6*z+8 = 0

z^2+6*z+8 = 0

DELTA = 6^2-(1*4*8)

DELTA = 4

DELTA > 0

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

z = -2 or z = -4

(z+4)*(z+2) = 0

1/(z+2)+3/(z+4)-2/((z+4)*(z+2)) = 0

(1*(z+4))/((z+2)*(z+4))+(3*(z+2))/((z+2)*(z+4))-2/((z+2)*(z+4)) = 0

1*(z+4)+3*(z+2)-2 = 0

4*z-2+10 = 0

4*z+8 = 0

(4*z+8)/((z+2)*(z+4)) = 0

(4*z+8)/((z+2)*(z+4)) = 0 // * (z+2)*(z+4)

4*z+8 = 0

4*z+8 = 0 // - 8

4*z = -8 // : 4

z = -8/4

z = -2

z in { -2} 

z belongs to the empty set

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