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

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

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

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

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

16*x^-2-5*x^-1-16 = 0

t_1 = x^-1

16*t_1^2-5*t_1^1-16 = 0

16*t_1^2-5*t_1-16 = 0

DELTA = (-5)^2-(-16*4*16)

DELTA = 1049

DELTA > 0

t_1 = (1049^(1/2)+5)/(2*16) or t_1 = (5-1049^(1/2))/(2*16)

t_1 = (1049^(1/2)+5)/32 or t_1 = (5-1049^(1/2))/32

t_1 = (5-1049^(1/2))/32

x^-1-((5-1049^(1/2))/32) = 0

1*x^-1 = (5-1049^(1/2))/32 // : 1

x^-1 = (5-1049^(1/2))/32

-1 < 0

1/(x^1) = (5-1049^(1/2))/32 // * x^1

1 = ((5-1049^(1/2))/32)*x^1 // : (5-1049^(1/2))/32

32*(5-1049^(1/2))^-1 = x^1

x = 32*(5-1049^(1/2))^-1

t_1 = (1049^(1/2)+5)/32

x^-1-((1049^(1/2)+5)/32) = 0

1*x^-1 = (1049^(1/2)+5)/32 // : 1

x^-1 = (1049^(1/2)+5)/32

-1 < 0

1/(x^1) = (1049^(1/2)+5)/32 // * x^1

1 = ((1049^(1/2)+5)/32)*x^1 // : (1049^(1/2)+5)/32

32*(1049^(1/2)+5)^-1 = x^1

x = 32*(1049^(1/2)+5)^-1

x in { 32*(5-1049^(1/2))^-1, 32*(1049^(1/2)+5)^-1 }

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