1+3/x+2=7/x^2-4

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Solution for 1+3/x+2=7/x^2-4 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)

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

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

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

3*x^-1-7*x^-2+7 = 0

t_1 = x^-1

3*t_1^1-7*t_1^2+7 = 0

3*t_1-7*t_1^2+7 = 0

DELTA = 3^2-(-7*4*7)

DELTA = 205

DELTA > 0

t_1 = (205^(1/2)-3)/(-7*2) or t_1 = (-205^(1/2)-3)/(-7*2)

t_1 = (205^(1/2)-3)/(-14) or t_1 = (205^(1/2)+3)/14

t_1 = (205^(1/2)-3)/(-14)

x^-1-((205^(1/2)-3)/(-14)) = 0

1*x^-1 = (205^(1/2)-3)/(-14) // : 1

x^-1 = (205^(1/2)-3)/(-14)

-1 < 0

1/(x^1) = (205^(1/2)-3)/(-14) // * x^1

1 = ((205^(1/2)-3)/(-14))*x^1 // : (205^(1/2)-3)/(-14)

-14*(205^(1/2)-3)^-1 = x^1

x = -14*(205^(1/2)-3)^-1

t_1 = (205^(1/2)+3)/14

x^-1-((205^(1/2)+3)/14) = 0

1*x^-1 = (205^(1/2)+3)/14 // : 1

x^-1 = (205^(1/2)+3)/14

-1 < 0

1/(x^1) = (205^(1/2)+3)/14 // * x^1

1 = ((205^(1/2)+3)/14)*x^1 // : (205^(1/2)+3)/14

14*(205^(1/2)+3)^-1 = x^1

x = 14*(205^(1/2)+3)^-1

x in { -14*(205^(1/2)-3)^-1, 14*(205^(1/2)+3)^-1 }

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