3/x+5-4/x+2=5/x^2+7x+10

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Solution for 3/x+5-4/x+2=5/x^2+7x+10 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-(4/x)+2+5 = 7*x+5/(x^2)+10 // - 7*x+5/(x^2)+10

3/x-(7*x)-(4/x)-(5/(x^2))-10+2+5 = 0

3/x-7*x-4*x^-1-5*x^-2-10+2+5 = 0

-7*x^1-1*x^-1-5*x^-2-3*x^0 = 0

(-7*x^3-3*x^2-1*x^1-5*x^0)/(x^2) = 0 // * x^4

x^2*(-7*x^3-3*x^2-1*x^1-5*x^0) = 0

x^2

-7*x^3-3*x^2-x-5 = 0

{ 1, -1, 5, -5 }

1

x = 1

-7*x^3-3*x^2-x-5 = -16

1

-1

x = -1

-7*x^3-3*x^2-x-5 = 0

-1

x+1

4*x-7*x^2-5

-7*x^3-3*x^2-x-5

x+1

7*x^3+7*x^2

4*x^2-x-5

-4*x^2-4*x

-5*x-5

5*x+5

0

4*x-7*x^2-5 = 0

DELTA = 4^2-(-7*(-5)*4)

DELTA = -124

DELTA < 0

x in { -1} 

x = -1

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