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

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


D( v )

v^2-1 = 0

3*v-3 = 0

v+1 = 0

v^2-1 = 0

v^2-1 = 0

1*v^2 = 1 // : 1

v^2 = 1

v^2 = 1 // ^ 1/2

abs(v) = 1

v = 1 or v = -1

3*v-3 = 0

3*v-3 = 0

3*v-3 = 0 // + 3

3*v = 3 // : 3

v = 3/3

v = 1

v+1 = 0

v+1 = 0

v+1 = 0 // - 1

v = -1

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

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

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

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

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

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

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

9*v^3+v^3-21*v^2+v^2-9*v-v-1+21 = 0

10*v^3-20*v^2-10*v+20 = 0

10*v^3-20*v^2-10*v+20 = 0

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

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

{ 1, -1, 2, -2 }

1

v = 1

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

1

v-1

v^2-v-2

v^3-2*v^2-v+2

v-1

v^2-v^3

2-v^2-v

v^2-v

2-2*v

2*v-2

0

v^2-v-2 = 0

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

DELTA = 9

DELTA > 0

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

v = 2 or v = -1

v in { -1, 2, 1} 

10*(v+1)*(v-2)*(v-1) = 0

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

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

10*(v+1)*(v-2)*(v-1) = 0

( v+1 )

v+1 = 0 // - 1

v = -1

( v-1 )

v-1 = 0 // + 1

v = 1

( v-2 )

v-2 = 0 // + 2

v = 2

v in { -1} 

v in { 1} 

v = 2

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