9/x-2=5/x^2

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Solution for 9/x-2=5/x^2 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)

9/x-2 = 5/(x^2) // - 5/(x^2)

9/x-(5/(x^2))-2 = 0

9/x-5*x^-2-2 = 0

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

t_1 = x^-1

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

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

DELTA = 9^2-(-5*(-2)*4)

DELTA = 41

DELTA > 0

t_1 = (41^(1/2)-9)/(-5*2) or t_1 = (-41^(1/2)-9)/(-5*2)

t_1 = (41^(1/2)-9)/(-10) or t_1 = (41^(1/2)+9)/10

t_1 = (41^(1/2)-9)/(-10)

x^-1-((41^(1/2)-9)/(-10)) = 0

1*x^-1 = (41^(1/2)-9)/(-10) // : 1

x^-1 = (41^(1/2)-9)/(-10)

-1 < 0

1/(x^1) = (41^(1/2)-9)/(-10) // * x^1

1 = ((41^(1/2)-9)/(-10))*x^1 // : (41^(1/2)-9)/(-10)

-10*(41^(1/2)-9)^-1 = x^1

x = -10*(41^(1/2)-9)^-1

t_1 = (41^(1/2)+9)/10

x^-1-((41^(1/2)+9)/10) = 0

1*x^-1 = (41^(1/2)+9)/10 // : 1

x^-1 = (41^(1/2)+9)/10

-1 < 0

1/(x^1) = (41^(1/2)+9)/10 // * x^1

1 = ((41^(1/2)+9)/10)*x^1 // : (41^(1/2)+9)/10

10*(41^(1/2)+9)^-1 = x^1

x = 10*(41^(1/2)+9)^-1

x in { -10*(41^(1/2)-9)^-1, 10*(41^(1/2)+9)^-1 }

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