6/(v+3)+8/7v+18/(v^2+3v)

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Solution for 6/(v+3)+8/7v+18/(v^2+3v) equation: 


D( v )

v^2+3*v = 0

v+3 = 0

v^2+3*v = 0

v^2+3*v = 0

v^2+3*v = 0

DELTA = 3^2-(0*1*4)

DELTA = 9

DELTA > 0

v = (9^(1/2)-3)/(1*2) or v = (-9^(1/2)-3)/(1*2)

v = 0 or v = -3

v+3 = 0

v+3 = 0

v+3 = 0 // - 3

v = -3

v in (-oo:-3) U (-3:0) U (0:+oo)

6/(v+3)+18/(v^2+3*v)+(8/7)*v = 0

6/(v+3)+18/(v^2+3*v)+(8*v)/7 = 0

v^2+3*v = 0

v^2+3*v = 0

v*(v+3) = 0

v+3 = 0 // - 3

v = -3

v*(v+3) = 0

6/(v+3)+18/(v*(v+3))+(8*v)/7 = 0

(6*7*v)/(7*v*(v+3))+(7*18)/(7*v*(v+3))+(8*v*v*(v+3))/(7*v*(v+3)) = 0

8*v*v*(v+3)+6*7*v+7*18 = 0

8*v^3+24*v^2+42*v+126 = 0

8*v^3+24*v^2+42*v+126 = 0

2*(4*v^3+12*v^2+21*v+63) = 0

4*v^3+12*v^2+21*v+63

21*(v+3)+4*v^3+12*v^2

4*v^2*(v+3)+21*(v+3)

(4*v^2+21)*(v+3)

2*(4*v^2+21)*(v+3) = 0

(2*(4*v^2+21)*(v+3))/(7*v*(v+3)) = 0

(2*(4*v^2+21)*(v+3))/(7*v*(v+3)) = 0 // * 7*v*(v+3)

2*(4*v^2+21)*(v+3) = 0

( 4*v^2+21 )

4*v^2 = -21 // : 4

v^2 = -21/4

( v+3 )

v+3 = 0 // - 3

v = -3

v in { -3} 

v belongs to the empty set

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