(3/x^2-4)+(2/x-2)=13/5

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Solution for (3/x^2-4)+(2/x-2)=13/5 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)

2/x+3/(x^2)-4-2 = 13/5 // - 13/5

2/x+3/(x^2)-(13/5)-4-2 = 0

2/x+3/(x^2)-13/5-4-2 = 0

2*x^-1+3*x^-2-43/5 = 0

t_1 = x^-1

3*t_1^2+2*t_1^1-43/5 = 0

3*t_1^2+2*t_1-43/5 = 0

DELTA = 2^2-(-43/5*3*4)

DELTA = 536/5

DELTA > 0

t_1 = ((536/5)^(1/2)-2)/(2*3) or t_1 = (-(536/5)^(1/2)-2)/(2*3)

t_1 = ((536/5)^(1/2)-2)/6 or t_1 = (-((536/5)^(1/2)+2))/6

t_1 = (-((536/5)^(1/2)+2))/6

x^-1-((-((536/5)^(1/2)+2))/6) = 0

x^-1+(1/6)*((536/5)^(1/2)+2) = 0

1*x^-1 = -(1/6*((536/5)^(1/2)+2)) // : 1

x^-1 = -1/6*((536/5)^(1/2)+2)

-1 < 0

1/(x^1) = -1/6*((536/5)^(1/2)+2) // * x^1

1 = -1/6*((536/5)^(1/2)+2)*x^1 // : -1/6*((536/5)^(1/2)+2)

-6*((536/5)^(1/2)+2)^-1 = x^1

x = -6*((536/5)^(1/2)+2)^-1

t_1 = ((536/5)^(1/2)-2)/6

x^-1-(((536/5)^(1/2)-2)/6) = 0

1*x^-1 = ((536/5)^(1/2)-2)/6 // : 1

x^-1 = ((536/5)^(1/2)-2)/6

-1 < 0

1/(x^1) = ((536/5)^(1/2)-2)/6 // * x^1

1 = (((536/5)^(1/2)-2)/6)*x^1 // : ((536/5)^(1/2)-2)/6

6*((536/5)^(1/2)-2)^-1 = x^1

x = 6*((536/5)^(1/2)-2)^-1

x in { -6*((536/5)^(1/2)+2)^-1, 6*((536/5)^(1/2)-2)^-1 }

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