10/x-3=60/x^2-9

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Solution for 10/x-3=60/x^2-9 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)

10/x-3 = 60/(x^2)-9 // - 60/(x^2)-9

10/x-(60/(x^2))-3+9 = 0

10/x-60*x^-2-3+9 = 0

10*x^-1-60*x^-2+6 = 0

t_1 = x^-1

10*t_1^1-60*t_1^2+6 = 0

10*t_1-60*t_1^2+6 = 0

DELTA = 10^2-(-60*4*6)

DELTA = 1540

DELTA > 0

t_1 = (1540^(1/2)-10)/(-60*2) or t_1 = (-1540^(1/2)-10)/(-60*2)

t_1 = (2*385^(1/2)-10)/(-120) or t_1 = (-2*385^(1/2)-10)/(-120)

t_1 = (2*385^(1/2)-10)/(-120)

x^-1-((2*385^(1/2)-10)/(-120)) = 0

1*x^-1 = (2*385^(1/2)-10)/(-120) // : 1

x^-1 = (2*385^(1/2)-10)/(-120)

-1 < 0

1/(x^1) = (2*385^(1/2)-10)/(-120) // * x^1

1 = ((2*385^(1/2)-10)/(-120))*x^1 // : (2*385^(1/2)-10)/(-120)

-120*(2*385^(1/2)-10)^-1 = x^1

x = -120*(2*385^(1/2)-10)^-1

t_1 = (-2*385^(1/2)-10)/(-120)

x^-1-((-2*385^(1/2)-10)/(-120)) = 0

1*x^-1 = (-2*385^(1/2)-10)/(-120) // : 1

x^-1 = (-2*385^(1/2)-10)/(-120)

-1 < 0

1/(x^1) = (-2*385^(1/2)-10)/(-120) // * x^1

1 = ((-2*385^(1/2)-10)/(-120))*x^1 // : (-2*385^(1/2)-10)/(-120)

-120*(-2*385^(1/2)-10)^-1 = x^1

x = -120*(-2*385^(1/2)-10)^-1

x in { -120*(2*385^(1/2)-10)^-1, -120*(-2*385^(1/2)-10)^-1 }

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