((x+9)/(x+2))=((5)/(x+2))+((44)/(x^(2)-4))

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Solution for ((x+9)/(x+2))=((5)/(x+2))+((44)/(x^(2)-4)) equation: 


D( x )

x+2 = 0

x^2-4 = 0

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

x^2-4 = 0

x^2-4 = 0

1*x^2 = 4 // : 1

x^2 = 4

x^2 = 4 // ^ 1/2

abs(x) = 2

x = 2 or x = -2

x in (-oo:-2) U (-2:2) U (2:+oo)

(x+9)/(x+2) = 5/(x+2)+44/(x^2-4) // - 5/(x+2)+44/(x^2-4)

(x+9)/(x+2)-(5/(x+2))-(44/(x^2-4)) = 0

(x+9)/(x+2)-5*(x+2)^-1-44*(x^2-4)^-1 = 0

(x+9)/(x+2)-5/(x+2)-44/(x^2-4) = 0

((x+9)*(x^2-4))/((x+2)*(x^2-4))+(-5*(x^2-4))/((x+2)*(x^2-4))+(-44*(x+2))/((x+2)*(x^2-4)) = 0

(x+9)*(x^2-4)-5*(x^2-4)-44*(x+2) = 0

x^3+4*x^2-4*x-44*x-88-16 = 0

x^3+4*x^2-48*x-104 = 0

x^3+4*x^2-48*x-104 = 0

x^3+4*x^2-48*x-104 = 0

{ 1, -1, 2, -2, 4, -4, 8, -8, 13, -13, 26, -26, 52, -52, 104, -104 }

1

x = 1

x^3+4*x^2-48*x-104 = -147

1

-1

x = -1

x^3+4*x^2-48*x-104 = -53

-1

2

x = 2

x^3+4*x^2-48*x-104 = -176

2

-2

x = -2

x^3+4*x^2-48*x-104 = 0

-2

x+2

x^2+2*x-52

x^3+4*x^2-48*x-104

x+2

-x^3-2*x^2

2*x^2-48*x-104

-2*x^2-4*x

-52*x-104

52*x+104

0

x^2+2*x-52 = 0

DELTA = 2^2-(-52*1*4)

DELTA = 212

DELTA > 0

x = (212^(1/2)-2)/(1*2) or x = (-212^(1/2)-2)/(1*2)

x = (2*53^(1/2)-2)/2 or x = (-2*53^(1/2)-2)/2

x in { (-2*53^(1/2)-2)/2, (2*53^(1/2)-2)/2, -2} 

(x-((-2*53^(1/2)-2)/2))*(x-((2*53^(1/2)-2)/2))*(x+2) = 0

((x-((-2*53^(1/2)-2)/2))*(x-((2*53^(1/2)-2)/2))*(x+2))/((x+2)*(x^2-4)) = 0

((x-((-2*53^(1/2)-2)/2))*(x-((2*53^(1/2)-2)/2))*(x+2))/((x+2)*(x^2-4)) = 0 // * (x+2)*(x^2-4)

(x-((-2*53^(1/2)-2)/2))*(x-((2*53^(1/2)-2)/2))*(x+2) = 0

( x+2 )

x+2 = 0 // - 2

x = -2

( x-((-2*53^(1/2)-2)/2) )

x-((-2*53^(1/2)-2)/2) = 0 // + (-2*53^(1/2)-2)/2

x = (-2*53^(1/2)-2)/2

( x-((2*53^(1/2)-2)/2) )

x-((2*53^(1/2)-2)/2) = 0 // + (2*53^(1/2)-2)/2

x = (2*53^(1/2)-2)/2

x in { -2} 

x in { (-2*53^(1/2)-2)/2, (2*53^(1/2)-2)/2 }

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