(x+8)/(x-2)=8/(x+2)+40/(x^2-4)

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Solution for (x+8)/(x-2)=8/(x+2)+40/(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+8)/(x-2) = 8/(x+2)+40/(x^2-4) // - 8/(x+2)+40/(x^2-4)

(x+8)/(x-2)-(8/(x+2))-(40/(x^2-4)) = 0

(x+8)/(x-2)-8*(x+2)^-1-40*(x^2-4)^-1 = 0

(x+8)/(x-2)-8/(x+2)-40/(x^2-4) = 0

((x+8)*(x+2)*(x^2-4))/((x-2)*(x+2)*(x^2-4))+(-8*(x-2)*(x^2-4))/((x-2)*(x+2)*(x^2-4))+(-40*(x-2)*(x+2))/((x-2)*(x+2)*(x^2-4)) = 0

(x+8)*(x+2)*(x^2-4)-8*(x-2)*(x^2-4)-40*(x-2)*(x+2) = 0

x^4+2*x^3+28*x^2-40*x^2-8*x-128+160 = 0

x^4+2*x^3-12*x^2-8*x+32 = 0

x^4+2*x^3-12*x^2-8*x+32 = 0

x^4+2*x^3-12*x^2-8*x+32 = 0

{ 1, -1, 2, -2, 4, -4, 8, -8, 16, -16, 32, -32 }

1

x = 1

x^4+2*x^3-12*x^2-8*x+32 = 15

1

-1

x = -1

x^4+2*x^3-12*x^2-8*x+32 = 27

-1

2

x = 2

x^4+2*x^3-12*x^2-8*x+32 = 0

2

x-2

x^3+4*x^2-4*x-16

x^4+2*x^3-12*x^2-8*x+32

x-2

2*x^3-x^4

4*x^3-12*x^2-8*x+32

8*x^2-4*x^3

32-4*x^2-8*x

4*x^2-8*x

32-16*x

16*x-32

0

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

{ 1, -1, 2, -2, 4, -4, 8, -8, 16, -16 }

1

x = 1

x^3+4*x^2-4*x-16 = -15

1

-1

x = -1

x^3+4*x^2-4*x-16 = -9

-1

2

x = 2

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

2

x-2

x^2+6*x+8

x^3+4*x^2-4*x-16

x-2

2*x^2-x^3

6*x^2-4*x-16

12*x-6*x^2

8*x-16

16-8*x

0

x^2+6*x+8 = 0

DELTA = 6^2-(1*4*8)

DELTA = 4

DELTA > 0

x = (4^(1/2)-6)/(1*2) or x = (-4^(1/2)-6)/(1*2)

x = -2 or x = -4

x in { -4, -2, 2, 2} 

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

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

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

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

( x+2 )

x+2 = 0 // - 2

x = -2

( x+4 )

x+4 = 0 // - 4

x = -4

( x-2 )

x-2 = 0 // + 2

x = 2

x in { -2} 

x in { 2} 

x = -4

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