1/x-2+3/x+3=10/x^2-9

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Solution for 1/x-2+3/x+3=10/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)

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

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

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

4*x^-1-10*x^-2+10 = 0

t_1 = x^-1

4*t_1^1-10*t_1^2+10 = 0

4*t_1-10*t_1^2+10 = 0

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

DELTA = 416

DELTA > 0

t_1 = (416^(1/2)-4)/(-10*2) or t_1 = (-416^(1/2)-4)/(-10*2)

t_1 = (4*26^(1/2)-4)/(-20) or t_1 = (-4*26^(1/2)-4)/(-20)

t_1 = (4*26^(1/2)-4)/(-20)

x^-1-((4*26^(1/2)-4)/(-20)) = 0

1*x^-1 = (4*26^(1/2)-4)/(-20) // : 1

x^-1 = (4*26^(1/2)-4)/(-20)

-1 < 0

1/(x^1) = (4*26^(1/2)-4)/(-20) // * x^1

1 = ((4*26^(1/2)-4)/(-20))*x^1 // : (4*26^(1/2)-4)/(-20)

-20*(4*26^(1/2)-4)^-1 = x^1

x = -20*(4*26^(1/2)-4)^-1

t_1 = (-4*26^(1/2)-4)/(-20)

x^-1-((-4*26^(1/2)-4)/(-20)) = 0

1*x^-1 = (-4*26^(1/2)-4)/(-20) // : 1

x^-1 = (-4*26^(1/2)-4)/(-20)

-1 < 0

1/(x^1) = (-4*26^(1/2)-4)/(-20) // * x^1

1 = ((-4*26^(1/2)-4)/(-20))*x^1 // : (-4*26^(1/2)-4)/(-20)

-20*(-4*26^(1/2)-4)^-1 = x^1

x = -20*(-4*26^(1/2)-4)^-1

x in { -20*(4*26^(1/2)-4)^-1, -20*(-4*26^(1/2)-4)^-1 }

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