((3-v)/(v-8))-((9v-7)/(8-v))=v

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Solution for ((3-v)/(v-8))-((9v-7)/(8-v))=v equation: 


D( v )

v-8 = 0

8-v = 0

v-8 = 0

v-8 = 0

v-8 = 0 // + 8

v = 8

8-v = 0

8-v = 0

8-v = 0 // - 8

-v = -8 // * -1

v = 8

v in (-oo:8) U (8:+oo)

(3-v)/(v-8)-((9*v-7)/(8-v)) = v // - v

(3-v)/(v-8)-((9*v-7)/(8-v))-v = 0

(3-v)/(v-8)+(-1*(9*v-7))/(8-v)-v = 0

((3-v)*(8-v))/((v-8)*(8-v))+(-1*(9*v-7)*(v-8))/((v-8)*(8-v))+(-v*(v-8)*(8-v))/((v-8)*(8-v)) = 0

(3-v)*(8-v)-1*(9*v-7)*(v-8)-v*(v-8)*(8-v) = 0

v^3-8*v^2-16*v^2+68*v+64*v-32 = 0

v^3-24*v^2+132*v-32 = 0

v^3-24*v^2+132*v-32 = 0

v^3-24*v^2+132*v-32 = 0

{ 1, -1, 2, -2, 4, -4, 8, -8, 16, -16, 32, -32 }

1

v = 1

v^3-24*v^2+132*v-32 = 77

1

-1

v = -1

v^3-24*v^2+132*v-32 = -189

-1

2

v = 2

v^3-24*v^2+132*v-32 = 144

2

-2

v = -2

v^3-24*v^2+132*v-32 = -400

-2

4

v = 4

v^3-24*v^2+132*v-32 = 176

4

-4

v = -4

v^3-24*v^2+132*v-32 = -1008

-4

8

v = 8

v^3-24*v^2+132*v-32 = 0

8

v-8

v^2-16*v+4

v^3-24*v^2+132*v-32

v-8

8*v^2-v^3

132*v-16*v^2-32

16*v^2-128*v

4*v-32

32-4*v

0

v^2-16*v+4 = 0

DELTA = (-16)^2-(1*4*4)

DELTA = 240

DELTA > 0

v = (240^(1/2)+16)/(1*2) or v = (16-240^(1/2))/(1*2)

v = (4*15^(1/2)+16)/2 or v = (16-4*15^(1/2))/2

v in { (16-4*15^(1/2))/2, (4*15^(1/2)+16)/2, 8} 

(v-((16-4*15^(1/2))/2))*(v-((4*15^(1/2)+16)/2))*(v-8) = 0

((v-((16-4*15^(1/2))/2))*(v-((4*15^(1/2)+16)/2))*(v-8))/((v-8)*(8-v)) = 0

((v-((16-4*15^(1/2))/2))*(v-((4*15^(1/2)+16)/2))*(v-8))/((v-8)*(8-v)) = 0 // * (v-8)*(8-v)

(v-((16-4*15^(1/2))/2))*(v-((4*15^(1/2)+16)/2))*(v-8) = 0

( v-((16-4*15^(1/2))/2) )

v-((16-4*15^(1/2))/2) = 0 // + (16-4*15^(1/2))/2

v = (16-4*15^(1/2))/2

( v-((4*15^(1/2)+16)/2) )

v-((4*15^(1/2)+16)/2) = 0 // + (4*15^(1/2)+16)/2

v = (4*15^(1/2)+16)/2

( v-8 )

v-8 = 0 // + 8

v = 8

v in { 8} 

v in { (16-4*15^(1/2))/2, (4*15^(1/2)+16)/2 }

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