3/x+4+1/x-4=16/x^2-16

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Solution for 3/x+4+1/x-4=16/x^2-16 equation:


D( x )

x = 0

x^2 = 0

x = 0

x = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

3/x+1/x-4+4 = 16/(x^2)-16 // - 16/(x^2)-16

3/x+1/x-(16/(x^2))-4+4+16 = 0

3/x+1/x-16*x^-2-4+4+16 = 0

4*x^-1-16*x^-2+16 = 0

t_1 = x^-1

4*t_1^1-16*t_1^2+16 = 0

4*t_1-16*t_1^2+16 = 0

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

DELTA = 1040

DELTA > 0

t_1 = (1040^(1/2)-4)/(-16*2) or t_1 = (-1040^(1/2)-4)/(-16*2)

t_1 = (4*65^(1/2)-4)/(-32) or t_1 = (-4*65^(1/2)-4)/(-32)

t_1 = (4*65^(1/2)-4)/(-32)

x^-1-((4*65^(1/2)-4)/(-32)) = 0

1*x^-1 = (4*65^(1/2)-4)/(-32) // : 1

x^-1 = (4*65^(1/2)-4)/(-32)

-1 < 0

1/(x^1) = (4*65^(1/2)-4)/(-32) // * x^1

1 = ((4*65^(1/2)-4)/(-32))*x^1 // : (4*65^(1/2)-4)/(-32)

-32*(4*65^(1/2)-4)^-1 = x^1

x = -32*(4*65^(1/2)-4)^-1

t_1 = (-4*65^(1/2)-4)/(-32)

x^-1-((-4*65^(1/2)-4)/(-32)) = 0

1*x^-1 = (-4*65^(1/2)-4)/(-32) // : 1

x^-1 = (-4*65^(1/2)-4)/(-32)

-1 < 0

1/(x^1) = (-4*65^(1/2)-4)/(-32) // * x^1

1 = ((-4*65^(1/2)-4)/(-32))*x^1 // : (-4*65^(1/2)-4)/(-32)

-32*(-4*65^(1/2)-4)^-1 = x^1

x = -32*(-4*65^(1/2)-4)^-1

x in { -32*(4*65^(1/2)-4)^-1, -32*(-4*65^(1/2)-4)^-1 }

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