7/x+4-5/x-4=12/x^2-16

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Solution for 7/x+4-5/x-4=12/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)

7/x-(5/x)-4+4 = 12/(x^2)-16 // - 12/(x^2)-16

7/x-(5/x)-(12/(x^2))-4+4+16 = 0

7/x-5*x^-1-12*x^-2-4+4+16 = 0

2*x^-1-12*x^-2+16 = 0

t_1 = x^-1

2*t_1^1-12*t_1^2+16 = 0

2*t_1-12*t_1^2+16 = 0

DELTA = 2^2-(-12*4*16)

DELTA = 772

DELTA > 0

t_1 = (772^(1/2)-2)/(-12*2) or t_1 = (-772^(1/2)-2)/(-12*2)

t_1 = (2*193^(1/2)-2)/(-24) or t_1 = (-2*193^(1/2)-2)/(-24)

t_1 = (2*193^(1/2)-2)/(-24)

x^-1-((2*193^(1/2)-2)/(-24)) = 0

1*x^-1 = (2*193^(1/2)-2)/(-24) // : 1

x^-1 = (2*193^(1/2)-2)/(-24)

-1 < 0

1/(x^1) = (2*193^(1/2)-2)/(-24) // * x^1

1 = ((2*193^(1/2)-2)/(-24))*x^1 // : (2*193^(1/2)-2)/(-24)

-24*(2*193^(1/2)-2)^-1 = x^1

x = -24*(2*193^(1/2)-2)^-1

t_1 = (-2*193^(1/2)-2)/(-24)

x^-1-((-2*193^(1/2)-2)/(-24)) = 0

1*x^-1 = (-2*193^(1/2)-2)/(-24) // : 1

x^-1 = (-2*193^(1/2)-2)/(-24)

-1 < 0

1/(x^1) = (-2*193^(1/2)-2)/(-24) // * x^1

1 = ((-2*193^(1/2)-2)/(-24))*x^1 // : (-2*193^(1/2)-2)/(-24)

-24*(-2*193^(1/2)-2)^-1 = x^1

x = -24*(-2*193^(1/2)-2)^-1

x in { -24*(2*193^(1/2)-2)^-1, -24*(-2*193^(1/2)-2)^-1 }

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