4-(3/v-2)=-3/(v-1)(v-2)

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Solution for 4-(3/v-2)=-3/(v-1)(v-2) equation: 


D( v )

v = 0

v-1 = 0

v = 0

v = 0

v-1 = 0

v-1 = 0

v-1 = 0 // + 1

v = 1

v in (-oo:0) U (0:1) U (1:+oo)

2-(3/v)+4 = (-3/(v-1))*(v-2) // - (-3/(v-1))*(v-2)

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

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

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

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

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

3*v^2+2*v^2+4*v^2-9*v-2*v-4*v+3 = 0

5*v^2+4*v^2-11*v-4*v+3 = 0

9*v^2-15*v+3 = 0

9*v^2-15*v+3 = 0

3*(3*v^2-5*v+1) = 0

3*v^2-5*v+1 = 0

DELTA = (-5)^2-(1*3*4)

DELTA = 13

DELTA > 0

v = (13^(1/2)+5)/(2*3) or v = (5-13^(1/2))/(2*3)

v = (13^(1/2)+5)/6 or v = (5-13^(1/2))/6

3*(v-((5-13^(1/2))/6))*(v-((13^(1/2)+5)/6)) = 0

(3*(v-((5-13^(1/2))/6))*(v-((13^(1/2)+5)/6)))/(v*(v-1)) = 0

(3*(v-((5-13^(1/2))/6))*(v-((13^(1/2)+5)/6)))/(v*(v-1)) = 0 // * v*(v-1)

3*(v-((5-13^(1/2))/6))*(v-((13^(1/2)+5)/6)) = 0

( v-((13^(1/2)+5)/6) )

v-((13^(1/2)+5)/6) = 0 // + (13^(1/2)+5)/6

v = (13^(1/2)+5)/6

( v-((5-13^(1/2))/6) )

v-((5-13^(1/2))/6) = 0 // + (5-13^(1/2))/6

v = (5-13^(1/2))/6

v in { (13^(1/2)+5)/6, (5-13^(1/2))/6 }

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