4/y-1/(y-1)^2=13/12

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Solution for 4/y-1/(y-1)^2=13/12 equation:


D( y )

y = 0

(y-1)^2 = 0

y = 0

y = 0

(y-1)^2 = 0

(y-1)^2 = 0

y-1 = 0 // + 1

y = 1

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

4/y-(1/((y-1)^2)) = 13/12 // - 13/12

4/y-(1/((y-1)^2))-(13/12) = 0

4/y-(y-1)^-2-13/12 = 0

4/y-1/((y-1)^2)-13/12 = 0

(-1*12*y)/(12*y*(y-1)^2)+(4*12*(y-1)^2)/(12*y*(y-1)^2)+(-13*y*(y-1)^2)/(12*y*(y-1)^2) = 0

4*12*(y-1)^2-13*y*(y-1)^2-1*12*y = 0

48*y^2-13*y^3+26*y^2-108*y-13*y+48 = 0

74*y^2-13*y^3-121*y+48 = 0

74*y^2-13*y^3-121*y+48 = 0

74*y^2-13*y^3-121*y+48 = 0

{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 12, -12, 16, -16, 24, -24, 48, -48 }

1

y = 1

74*y^2-13*y^3-121*y+48 = -12

1

-1

y = -1

74*y^2-13*y^3-121*y+48 = 256

-1

2

y = 2

74*y^2-13*y^3-121*y+48 = -2

2

-2

y = -2

74*y^2-13*y^3-121*y+48 = 690

-2

3

y = 3

74*y^2-13*y^3-121*y+48 = 0

3

y-3

35*y-13*y^2-16

74*y^2-13*y^3-121*y+48

y-3

13*y^3-39*y^2

35*y^2-121*y+48

105*y-35*y^2

48-16*y

16*y-48

0

35*y-13*y^2-16 = 0

DELTA = 35^2-(-16*(-13)*4)

DELTA = 393

DELTA > 0

y = (393^(1/2)-35)/(-13*2) or y = (-393^(1/2)-35)/(-13*2)

y = (393^(1/2)-35)/(-26) or y = (393^(1/2)+35)/26

y in { (393^(1/2)-35)/(-26), (393^(1/2)+35)/26, 3}

(y-((393^(1/2)-35)/(-26)))*(y-((393^(1/2)+35)/26))*(y-3) = 0

((y-((393^(1/2)-35)/(-26)))*(y-((393^(1/2)+35)/26))*(y-3))/(12*y*(y-1)^2) = 0

((y-((393^(1/2)-35)/(-26)))*(y-((393^(1/2)+35)/26))*(y-3))/(12*y*(y-1)^2) = 0 // * 12*y*(y-1)^2

(y-((393^(1/2)-35)/(-26)))*(y-((393^(1/2)+35)/26))*(y-3) = 0

( y-((393^(1/2)+35)/26) )

y-((393^(1/2)+35)/26) = 0 // + (393^(1/2)+35)/26

y = (393^(1/2)+35)/26

( y-((393^(1/2)-35)/(-26)) )

y-((393^(1/2)-35)/(-26)) = 0 // + (393^(1/2)-35)/(-26)

y = (393^(1/2)-35)/(-26)

( y-3 )

y-3 = 0 // + 3

y = 3

y in { (393^(1/2)+35)/26, (393^(1/2)-35)/(-26), 3 }

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