4/x-3+9/x^2-9=7/x+3

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Solution for 4/x-3+9/x^2-9=7/x+3 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)

4/x+9/(x^2)-9-3 = 7/x+3 // - 7/x+3

4/x-(7/x)+9/(x^2)-9-3-3 = 0

4/x-7*x^-1+9/(x^2)-9-3-3 = 0

9*x^-2-3*x^-1-15 = 0

t_1 = x^-1

9*t_1^2-3*t_1^1-15 = 0

9*t_1^2-3*t_1-15 = 0

DELTA = (-3)^2-(-15*4*9)

DELTA = 549

DELTA > 0

t_1 = (549^(1/2)+3)/(2*9) or t_1 = (3-549^(1/2))/(2*9)

t_1 = (3*61^(1/2)+3)/18 or t_1 = (3-3*61^(1/2))/18

t_1 = (3-3*61^(1/2))/18

x^-1-((3-3*61^(1/2))/18) = 0

1*x^-1 = (3-3*61^(1/2))/18 // : 1

x^-1 = (3-3*61^(1/2))/18

-1 < 0

1/(x^1) = (3-3*61^(1/2))/18 // * x^1

1 = ((3-3*61^(1/2))/18)*x^1 // : (3-3*61^(1/2))/18

18*(3-3*61^(1/2))^-1 = x^1

x = 18*(3-3*61^(1/2))^-1

t_1 = (3*61^(1/2)+3)/18

x^-1-((3*61^(1/2)+3)/18) = 0

1*x^-1 = (3*61^(1/2)+3)/18 // : 1

x^-1 = (3*61^(1/2)+3)/18

-1 < 0

1/(x^1) = (3*61^(1/2)+3)/18 // * x^1

1 = ((3*61^(1/2)+3)/18)*x^1 // : (3*61^(1/2)+3)/18

18*(3*61^(1/2)+3)^-1 = x^1

x = 18*(3*61^(1/2)+3)^-1

x in { 18*(3-3*61^(1/2))^-1, 18*(3*61^(1/2)+3)^-1 }

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