6/(v-6)-(3v)/(2v-4)

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Solution for 6/(v-6)-(3v)/(2v-4) equation: 


D( v )

2*v-4 = 0

v-6 = 0

2*v-4 = 0

2*v-4 = 0

2*v-4 = 0 // + 4

2*v = 4 // : 2

v = 4/2

v = 2

v-6 = 0

v-6 = 0

v-6 = 0 // + 6

v = 6

v in (-oo:2) U (2:6) U (6:+oo)

6/(v-6)-((3*v)/(2*v-4)) = 0

6/(v-6)-3*v*(2*v-4)^-1 = 0

6/(v-6)+(-3*v)/(2*v-4) = 0

(6*(2*v-4))/((v-6)*(2*v-4))+(-3*v*(v-6))/((v-6)*(2*v-4)) = 0

6*(2*v-4)-3*v*(v-6) = 0

30*v-3*v^2-24 = 0

30*v-3*v^2-24 = 0

3*(10*v-v^2-8) = 0

10*v-v^2-8 = 0

DELTA = 10^2-(-8*(-1)*4)

DELTA = 68

DELTA > 0

v = (68^(1/2)-10)/(-1*2) or v = (-68^(1/2)-10)/(-1*2)

v = (2*17^(1/2)-10)/(-2) or v = (-2*17^(1/2)-10)/(-2)

3*(v-((2*17^(1/2)-10)/(-2)))*(v-((-2*17^(1/2)-10)/(-2))) = 0

(3*(v-((2*17^(1/2)-10)/(-2)))*(v-((-2*17^(1/2)-10)/(-2))))/((v-6)*(2*v-4)) = 0

(3*(v-((2*17^(1/2)-10)/(-2)))*(v-((-2*17^(1/2)-10)/(-2))))/((v-6)*(2*v-4)) = 0 // * (v-6)*(2*v-4)

3*(v-((2*17^(1/2)-10)/(-2)))*(v-((-2*17^(1/2)-10)/(-2))) = 0

( 3 )

3 = 0

v belongs to the empty set

( v-((-2*17^(1/2)-10)/(-2)) )

v-((-2*17^(1/2)-10)/(-2)) = 0 // + (-2*17^(1/2)-10)/(-2)

v = (-2*17^(1/2)-10)/(-2)

( v-((2*17^(1/2)-10)/(-2)) )

v-((2*17^(1/2)-10)/(-2)) = 0 // + (2*17^(1/2)-10)/(-2)

v = (2*17^(1/2)-10)/(-2)

v in { (-2*17^(1/2)-10)/(-2), (2*17^(1/2)-10)/(-2) }

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