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

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


D( x )

x+2 = 0

x-2 = 0

x^2-4 = 0

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

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

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

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

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

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

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

x^4+9*x^3+18*x^2-44*x^2-36*x-88+176 = 0

x^4+9*x^3-26*x^2-36*x+88 = 0

x^4+9*x^3-26*x^2-36*x+88 = 0

x^4+9*x^3-26*x^2-36*x+88 = 0

{ 1, -1, 2, -2, 4, -4, 8, -8, 11, -11, 22, -22, 44, -44, 88, -88 }

1

x = 1

x^4+9*x^3-26*x^2-36*x+88 = 36

1

-1

x = -1

x^4+9*x^3-26*x^2-36*x+88 = 90

-1

2

x = 2

x^4+9*x^3-26*x^2-36*x+88 = 0

2

x-2

x^3+11*x^2-4*x-44

x^4+9*x^3-26*x^2-36*x+88

x-2

2*x^3-x^4

11*x^3-26*x^2-36*x+88

22*x^2-11*x^3

88-4*x^2-36*x

4*x^2-8*x

88-44*x

44*x-88

0

x^3+11*x^2-4*x-44 = 0

{ 1, -1, 2, -2, 4, -4, 11, -11, 22, -22, 44, -44 }

1

x = 1

x^3+11*x^2-4*x-44 = -36

1

-1

x = -1

x^3+11*x^2-4*x-44 = -30

-1

2

x = 2

x^3+11*x^2-4*x-44 = 0

2

x-2

x^2+13*x+22

x^3+11*x^2-4*x-44

x-2

2*x^2-x^3

13*x^2-4*x-44

26*x-13*x^2

22*x-44

44-22*x

0

x^2+13*x+22 = 0

DELTA = 13^2-(1*4*22)

DELTA = 81

DELTA > 0

x = (81^(1/2)-13)/(1*2) or x = (-81^(1/2)-13)/(1*2)

x = -2 or x = -11

x in { -11, -2, 2, 2} 

(x+11)*(x+2)*(x-2)^2 = 0

((x+11)*(x+2)*(x-2)^2)/((x-2)*(x+2)*(x^2-4)) = 0

((x+11)*(x+2)*(x-2)^2)/((x-2)*(x+2)*(x^2-4)) = 0 // * (x-2)*(x+2)*(x^2-4)

(x+11)*(x+2)*(x-2)^2 = 0

( x+11 )

x+11 = 0 // - 11

x = -11

( x+2 )

x+2 = 0 // - 2

x = -2

( x-2 )

x-2 = 0 // + 2

x = 2

x in { -2} 

x in { 2} 

x = -11

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