(10x)/(x^2-64)-8/(x-8)=1/(x+8)

Solution for (10x)/(x^2-64)-8/(x-8)=1/(x+8) equation:

D( x )

x^2-64 = 0

x+8 = 0

x-8 = 0

x^2-64 = 0

x^2-64 = 0

1*x^2 = 64 // : 1

x^2 = 64

x^2 = 64 // ^ 1/2

abs(x) = 8

x = 8 or x = -8

x+8 = 0

x+8 = 0

x+8 = 0 // - 8

x = -8

x-8 = 0

x-8 = 0

x-8 = 0 // + 8

x = 8

x in (-oo:-8) U (-8:8) U (8:+oo)

(10*x)/(x^2-64)-(8/(x-8)) = 1/(x+8) // - 1/(x+8)

(10*x)/(x^2-64)-(8/(x-8))-(1/(x+8)) = 0

(10*x)/(x^2-64)-8*(x-8)^-1-(x+8)^-1 = 0

(10*x)/(x^2-64)-8/(x-8)-1/(x+8) = 0

(10*x*(x-8)*(x+8))/((x^2-64)*(x-8)*(x+8))+(-8*(x^2-64)*(x+8))/((x^2-64)*(x-8)*(x+8))+(-1*(x^2-64)*(x-8))/((x^2-64)*(x-8)*(x+8)) = 0

10*x*(x-8)*(x+8)-8*(x^2-64)*(x+8)-1*(x^2-64)*(x-8) = 0

2*x^3-x^3-64*x^2+8*x^2-128*x+64*x-512+4096 = 0

x^3-56*x^2-64*x+3584 = 0

x^3-56*x^2-64*x+3584 = 0

x^3-56*x^2-64*x+3584 = 0

{ 1, -1, 2, -2, 4, -4, 7, -7, 8, -8, 14, -14, 16, -16, 28, -28, 32, -32, 56, -56, 64, -64, 112, -112, 128, -128, 224, -224, 256, -256, 448, -448, 512, -512, 896, -896, 1792, -1792, 3584, -3584 }

1

x = 1

x^3-56*x^2-64*x+3584 = 3465

1

-1

x = -1

x^3-56*x^2-64*x+3584 = 3591

-1

2

x = 2

x^3-56*x^2-64*x+3584 = 3240

2

-2

x = -2

x^3-56*x^2-64*x+3584 = 3480

-2

4

x = 4

x^3-56*x^2-64*x+3584 = 2496

4

-4

x = -4

x^3-56*x^2-64*x+3584 = 2880

-4

7

x = 7

x^3-56*x^2-64*x+3584 = 735

7

-7

x = -7

x^3-56*x^2-64*x+3584 = 945

-7

8

x = 8

x^3-56*x^2-64*x+3584 = 0

8

x-8

x^2-48*x-448

x^3-56*x^2-64*x+3584

x-8

8*x^2-x^3

3584-48*x^2-64*x

48*x^2-384*x

3584-448*x

448*x-3584

0

x^2-48*x-448 = 0

DELTA = (-48)^2-(-448*1*4)

DELTA = 4096

DELTA > 0

x = (4096^(1/2)+48)/(1*2) or x = (48-4096^(1/2))/(1*2)

x = 56 or x = -8

x in { -8, 56, 8} 

(x+8)*(x-56)*(x-8) = 0

((x+8)*(x-56)*(x-8))/((x^2-64)*(x-8)*(x+8)) = 0

((x+8)*(x-56)*(x-8))/((x^2-64)*(x-8)*(x+8)) = 0 // * (x^2-64)*(x-8)*(x+8)

(x+8)*(x-56)*(x-8) = 0

( x+8 )

x+8 = 0 // - 8

x = -8

( x-56 )

x-56 = 0 // + 56

x = 56

( x-8 )

x-8 = 0 // + 8

x = 8

x in { -8} 

x in { 8} 

x = 56