((x+4)/(x-2))=(5/(x+2))+(24/((x^2)-4))

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Solution for ((x+4)/(x-2))=(5/(x+2))+(24/((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+4)/(x-2) = 5/(x+2)+24/(x^2-4) // - 5/(x+2)+24/(x^2-4)

(x+4)/(x-2)-(5/(x+2))-(24/(x^2-4)) = 0

(x+4)/(x-2)-5*(x+2)^-1-24*(x^2-4)^-1 = 0

(x+4)/(x-2)-5/(x+2)-24/(x^2-4) = 0

((x+4)*(x+2)*(x^2-4))/((x-2)*(x+2)*(x^2-4))+(-5*(x-2)*(x^2-4))/((x-2)*(x+2)*(x^2-4))+(-24*(x-2)*(x+2))/((x-2)*(x+2)*(x^2-4)) = 0

(x+4)*(x+2)*(x^2-4)-5*(x-2)*(x^2-4)-24*(x-2)*(x+2) = 0

x^4+x^3+14*x^2-24*x^2-4*x-72+96 = 0

x^4+x^3-10*x^2-4*x+24 = 0

x^4+x^3-10*x^2-4*x+24 = 0

x^4+x^3-10*x^2-4*x+24 = 0

{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 12, -12, 24, -24 }

1

x = 1

x^4+x^3-10*x^2-4*x+24 = 12

1

-1

x = -1

x^4+x^3-10*x^2-4*x+24 = 18

-1

2

x = 2

x^4+x^3-10*x^2-4*x+24 = 0

2

x-2

x^3+3*x^2-4*x-12

x^4+x^3-10*x^2-4*x+24

x-2

2*x^3-x^4

3*x^3-10*x^2-4*x+24

6*x^2-3*x^3

24-4*x^2-4*x

4*x^2-8*x

24-12*x

12*x-24

0

x^3+3*x^2-4*x-12 = 0

{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 12, -12 }

1

x = 1

x^3+3*x^2-4*x-12 = -12

1

-1

x = -1

x^3+3*x^2-4*x-12 = -6

-1

2

x = 2

x^3+3*x^2-4*x-12 = 0

2

x-2

x^2+5*x+6

x^3+3*x^2-4*x-12

x-2

2*x^2-x^3

5*x^2-4*x-12

10*x-5*x^2

6*x-12

12-6*x

0

x^2+5*x+6 = 0

DELTA = 5^2-(1*4*6)

DELTA = 1

DELTA > 0

x = (1^(1/2)-5)/(1*2) or x = (-1^(1/2)-5)/(1*2)

x = -2 or x = -3

x in { -3, -2, 2, 2} 

(x+3)*(x+2)*(x-2)^2 = 0

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

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

(x+3)*(x+2)*(x-2)^2 = 0

( x+2 )

x+2 = 0 // - 2

x = -2

( x+3 )

x+3 = 0 // - 3

x = -3

( x-2 )

x-2 = 0 // + 2

x = 2

x in { -2} 

x in { 2} 

x = -3

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