4/t-1=4/t^2-2

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Solution for 4/t-1=4/t^2-2 equation: 


D( t )

t^2 = 0

t = 0

t^2 = 0

t^2 = 0

1*t^2 = 0 // : 1

t^2 = 0

t = 0

t = 0

t = 0

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

4/t-1 = 4/(t^2)-2 // - 4/(t^2)-2

4/t-(4/(t^2))-1+2 = 0

4/t-4*t^-2-1+2 = 0

4*t^-1-4*t^-2+1 = 0

t_1 = t^-1

4*t_1^1-4*t_1^2+1 = 0

4*t_1-4*t_1^2+1 = 0

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

DELTA = 32

DELTA > 0

t_1 = (32^(1/2)-4)/(-4*2) or t_1 = (-32^(1/2)-4)/(-4*2)

t_1 = (4*2^(1/2)-4)/(-8) or t_1 = (-4*2^(1/2)-4)/(-8)

t_1 = (4*2^(1/2)-4)/(-8)

t^-1-((4*2^(1/2)-4)/(-8)) = 0

1*t^-1 = (4*2^(1/2)-4)/(-8) // : 1

t^-1 = (4*2^(1/2)-4)/(-8)

-1 < 0

1/(t^1) = (4*2^(1/2)-4)/(-8) // * t^1

1 = ((4*2^(1/2)-4)/(-8))*t^1 // : (4*2^(1/2)-4)/(-8)

-8*(4*2^(1/2)-4)^-1 = t^1

t = -8*(4*2^(1/2)-4)^-1

t_1 = (-4*2^(1/2)-4)/(-8)

t^-1-((-4*2^(1/2)-4)/(-8)) = 0

1*t^-1 = (-4*2^(1/2)-4)/(-8) // : 1

t^-1 = (-4*2^(1/2)-4)/(-8)

-1 < 0

1/(t^1) = (-4*2^(1/2)-4)/(-8) // * t^1

1 = ((-4*2^(1/2)-4)/(-8))*t^1 // : (-4*2^(1/2)-4)/(-8)

-8*(-4*2^(1/2)-4)^-1 = t^1

t = -8*(-4*2^(1/2)-4)^-1

t in { -8*(4*2^(1/2)-4)^-1, -8*(-4*2^(1/2)-4)^-1 }

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