((x+5)/(x-2))=(1/(x+2))+(28/(x^2-4))

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Solution for ((x+5)/(x-2))=(1/(x+2))+(28/(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+5)/(x-2) = 1/(x+2)+28/(x^2-4) // - 1/(x+2)+28/(x^2-4)

(x+5)/(x-2)-(1/(x+2))-(28/(x^2-4)) = 0

(x+5)/(x-2)-(x+2)^-1-28*(x^2-4)^-1 = 0

(x+5)/(x-2)-1/(x+2)-28/(x^2-4) = 0

((x+5)*(x+2)*(x^2-4))/((x-2)*(x+2)*(x^2-4))+(-1*(x-2)*(x^2-4))/((x-2)*(x+2)*(x^2-4))+(-28*(x-2)*(x+2))/((x-2)*(x+2)*(x^2-4)) = 0

(x+5)*(x+2)*(x^2-4)-1*(x-2)*(x^2-4)-28*(x-2)*(x+2) = 0

x^4+6*x^3+8*x^2-28*x^2-24*x-48+112 = 0

x^4+6*x^3-20*x^2-24*x+64 = 0

x^4+6*x^3-20*x^2-24*x+64 = 0

x^4+6*x^3-20*x^2-24*x+64 = 0

{ 1, -1, 2, -2, 4, -4, 8, -8, 16, -16, 32, -32, 64, -64 }

1

x = 1

x^4+6*x^3-20*x^2-24*x+64 = 27

1

-1

x = -1

x^4+6*x^3-20*x^2-24*x+64 = 63

-1

2

x = 2

x^4+6*x^3-20*x^2-24*x+64 = 0

2

x-2

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

x^4+6*x^3-20*x^2-24*x+64

x-2

2*x^3-x^4

8*x^3-20*x^2-24*x+64

16*x^2-8*x^3

64-4*x^2-24*x

4*x^2-8*x

64-32*x

32*x-64

0

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

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

1

x = 1

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

1

-1

x = -1

x^3+8*x^2-4*x-32 = -21

-1

2

x = 2

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

2

x-2

x^2+10*x+16

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

x-2

2*x^2-x^3

10*x^2-4*x-32

20*x-10*x^2

16*x-32

32-16*x

0

x^2+10*x+16 = 0

DELTA = 10^2-(1*4*16)

DELTA = 36

DELTA > 0

x = (36^(1/2)-10)/(1*2) or x = (-36^(1/2)-10)/(1*2)

x = -2 or x = -8

x in { -8, -2, 2, 2} 

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

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

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

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

( x+2 )

x+2 = 0 // - 2

x = -2

( x+8 )

x+8 = 0 // - 8

x = -8

( x-2 )

x-2 = 0 // + 2

x = 2

x in { -2} 

x in { 2} 

x = -8

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