(4y/y-3)-(12/y+3)=(72/y^2-9)

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Solution for (4y/y-3)-(12/y+3)=(72/y^2-9) equation:


D( y )

y = 0

y^2 = 0

y = 0

y = 0

y^2 = 0

y^2 = 0

1*y^2 = 0 // : 1

y^2 = 0

y = 0

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

(4*y)/y-(12/y)-3-3 = 72/(y^2)-9 // - 72/(y^2)-9

(4*y)/y-(12/y)-(72/(y^2))-3-3+9 = 0

(4*y)/y-12*y^-1-72*y^-2-3-3+9 = 0

7-12*y^-1-72*y^-2 = 0

t_1 = y^-1

7-72*t_1^2-12*t_1^1 = 0

7-72*t_1^2-12*t_1 = 0

DELTA = (-12)^2-(-72*4*7)

DELTA = 2160

DELTA > 0

t_1 = (2160^(1/2)+12)/(-72*2) or t_1 = (12-2160^(1/2))/(-72*2)

t_1 = (12*15^(1/2)+12)/(-144) or t_1 = (12-12*15^(1/2))/(-144)

t_1 = (12*15^(1/2)+12)/(-144)

y^-1-((12*15^(1/2)+12)/(-144)) = 0

1*y^-1 = (12*15^(1/2)+12)/(-144) // : 1

y^-1 = (12*15^(1/2)+12)/(-144)

-1 < 0

1/(y^1) = (12*15^(1/2)+12)/(-144) // * y^1

1 = ((12*15^(1/2)+12)/(-144))*y^1 // : (12*15^(1/2)+12)/(-144)

-144*(12*15^(1/2)+12)^-1 = y^1

y = -144*(12*15^(1/2)+12)^-1

t_1 = (12-12*15^(1/2))/(-144)

y^-1-((12-12*15^(1/2))/(-144)) = 0

1*y^-1 = (12-12*15^(1/2))/(-144) // : 1

y^-1 = (12-12*15^(1/2))/(-144)

-1 < 0

1/(y^1) = (12-12*15^(1/2))/(-144) // * y^1

1 = ((12-12*15^(1/2))/(-144))*y^1 // : (12-12*15^(1/2))/(-144)

-144*(12-12*15^(1/2))^-1 = y^1

y = -144*(12-12*15^(1/2))^-1

y in { -144*(12*15^(1/2)+12)^-1, -144*(12-12*15^(1/2))^-1 }

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