(x+3/x+2)+(5/x^2-x-6)

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Solution for (x+3/x+2)+(5/x^2-x-6) 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)

x-x+3/x+5/(x^2)-6+2 = 0

3*x^-1+5*x^-2-4 = 0

t_1 = x^-1

5*t_1^2+3*t_1^1-4 = 0

5*t_1^2+3*t_1-4 = 0

DELTA = 3^2-(-4*4*5)

DELTA = 89

DELTA > 0

t_1 = (89^(1/2)-3)/(2*5) or t_1 = (-89^(1/2)-3)/(2*5)

t_1 = (89^(1/2)-3)/10 or t_1 = (-(89^(1/2)+3))/10

t_1 = (-(89^(1/2)+3))/10

x^-1-((-(89^(1/2)+3))/10) = 0

x^-1+(1/10)*(89^(1/2)+3) = 0

1*x^-1 = -(1/10*(89^(1/2)+3)) // : 1

x^-1 = -1/10*(89^(1/2)+3)

-1 < 0

1/(x^1) = -1/10*(89^(1/2)+3) // * x^1

1 = -1/10*(89^(1/2)+3)*x^1 // : -1/10*(89^(1/2)+3)

-10*(89^(1/2)+3)^-1 = x^1

x = -10*(89^(1/2)+3)^-1

t_1 = (89^(1/2)-3)/10

x^-1-((89^(1/2)-3)/10) = 0

1*x^-1 = (89^(1/2)-3)/10 // : 1

x^-1 = (89^(1/2)-3)/10

-1 < 0

1/(x^1) = (89^(1/2)-3)/10 // * x^1

1 = ((89^(1/2)-3)/10)*x^1 // : (89^(1/2)-3)/10

10*(89^(1/2)-3)^-1 = x^1

x = 10*(89^(1/2)-3)^-1

x in { -10*(89^(1/2)+3)^-1, 10*(89^(1/2)-3)^-1 }

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