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

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Solution for (24/x^2-16)-(3/x-4)=(2/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)

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

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

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

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

t_1 = x^-1

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

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

DELTA = (-5)^2-(-16*4*24)

DELTA = 1561

DELTA > 0

t_1 = (1561^(1/2)+5)/(2*24) or t_1 = (5-1561^(1/2))/(2*24)

t_1 = (1561^(1/2)+5)/48 or t_1 = (5-1561^(1/2))/48

t_1 = (5-1561^(1/2))/48

x^-1-((5-1561^(1/2))/48) = 0

1*x^-1 = (5-1561^(1/2))/48 // : 1

x^-1 = (5-1561^(1/2))/48

-1 < 0

1/(x^1) = (5-1561^(1/2))/48 // * x^1

1 = ((5-1561^(1/2))/48)*x^1 // : (5-1561^(1/2))/48

48*(5-1561^(1/2))^-1 = x^1

x = 48*(5-1561^(1/2))^-1

t_1 = (1561^(1/2)+5)/48

x^-1-((1561^(1/2)+5)/48) = 0

1*x^-1 = (1561^(1/2)+5)/48 // : 1

x^-1 = (1561^(1/2)+5)/48

-1 < 0

1/(x^1) = (1561^(1/2)+5)/48 // * x^1

1 = ((1561^(1/2)+5)/48)*x^1 // : (1561^(1/2)+5)/48

48*(1561^(1/2)+5)^-1 = x^1

x = 48*(1561^(1/2)+5)^-1

x in { 48*(5-1561^(1/2))^-1, 48*(1561^(1/2)+5)^-1 }

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