(x/(x^2-16))-((x+2)/(x^2-4x))=(-5/(x^2+4x))

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Solution for (x/(x^2-16))-((x+2)/(x^2-4x))=(-5/(x^2+4x)) equation: 


D( x )

x^2-16 = 0

x^2-(4*x) = 0

x^2+4*x = 0

x^2-16 = 0

x^2-16 = 0

1*x^2 = 16 // : 1

x^2 = 16

x^2 = 16 // ^ 1/2

abs(x) = 4

x = 4 or x = -4

x^2-(4*x) = 0

x^2-(4*x) = 0

x^2-4*x = 0

x^2-4*x = 0

DELTA = (-4)^2-(0*1*4)

DELTA = 16

DELTA > 0

x = (16^(1/2)+4)/(1*2) or x = (4-16^(1/2))/(1*2)

x = 4 or x = 0

x^2+4*x = 0

x^2+4*x = 0

x^2+4*x = 0

DELTA = 4^2-(0*1*4)

DELTA = 16

DELTA > 0

x = (16^(1/2)-4)/(1*2) or x = (-16^(1/2)-4)/(1*2)

x = 0 or x = -4

x in (-oo:-4) U (-4:0) U (0:4) U (4:+oo)

x/(x^2-16)-((x+2)/(x^2-(4*x))) = -5/(x^2+4*x) // + -5/(x^2+4*x)

x/(x^2-16)-((x+2)/(x^2-(4*x)))-(-5/(x^2+4*x)) = 0

x/(x^2-16)-((x+2)/(x^2-4*x))+5*(x^2+4*x)^-1 = 0

x/(x^2-16)+(-1*(x+2))/(x^2-4*x)+5/(x^2+4*x) = 0

x^2-4*x = 0

x^2-4*x = 0

x*(x-4) = 0

x-4 = 0 // + 4

x = 4

x*(x-4) = 0

x^2+4*x = 0

x^2+4*x = 0

x*(x+4) = 0

x+4 = 0 // - 4

x = -4

x*(x+4) = 0

x/(x^2-16)+(-1*(x+2))/(x*(x-4))+5/(x*(x+4)) = 0

(x^2*(x-4))/(x*(x^2-16)*(x-4))+(-1*(x+2)*(x^2-16))/(x*(x^2-16)*(x-4))+(5*(x^2-16)*(x-4))/(x*(x^2-16)*(x-4)) = 0

x^2*(x-4)-1*(x+2)*(x^2-16)+5*(x^2-16)*(x-4) = 0

5*x^3-6*x^2-20*x^2+16*x-80*x+32+320 = 0

5*x^3-26*x^2-64*x+352 = 0

5*x^3-26*x^2-64*x+352 = 0

5*x^3-26*x^2-64*x+352 = 0

{ 1, -1, 2, -2, 4, -4, 8, -8, 11, -11, 16, -16, 22, -22, 32, -32, 44, -44, 88, -88, 176, -176, 352, -352 }

1

x = 1

5*x^3-26*x^2-64*x+352 = 267

1

-1

x = -1

5*x^3-26*x^2-64*x+352 = 385

-1

2

x = 2

5*x^3-26*x^2-64*x+352 = 160

2

-2

x = -2

5*x^3-26*x^2-64*x+352 = 336

-2

4

x = 4

5*x^3-26*x^2-64*x+352 = 0

4

x-4

5*x^2-6*x-88

5*x^3-26*x^2-64*x+352

x-4

20*x^2-5*x^3

352-6*x^2-64*x

6*x^2-24*x

352-88*x

88*x-352

0

5*x^2-6*x-88 = 0

DELTA = (-6)^2-(-88*4*5)

DELTA = 1796

DELTA > 0

x = (1796^(1/2)+6)/(2*5) or x = (6-1796^(1/2))/(2*5)

x = (2*449^(1/2)+6)/10 or x = (6-2*449^(1/2))/10

x in { (6-2*449^(1/2))/10, (2*449^(1/2)+6)/10, 4} 

(x-((6-2*449^(1/2))/10))*(x-((2*449^(1/2)+6)/10))*(x-4) = 0

((x-((6-2*449^(1/2))/10))*(x-((2*449^(1/2)+6)/10))*(x-4))/(x*(x^2-16)*(x-4)) = 0

((x-((6-2*449^(1/2))/10))*(x-((2*449^(1/2)+6)/10))*(x-4))/(x*(x^2-16)*(x-4)) = 0 // * x*(x^2-16)*(x-4)

(x-((6-2*449^(1/2))/10))*(x-((2*449^(1/2)+6)/10))*(x-4) = 0

( x-((2*449^(1/2)+6)/10) )

x-((2*449^(1/2)+6)/10) = 0 // + (2*449^(1/2)+6)/10

x = (2*449^(1/2)+6)/10

( x-((6-2*449^(1/2))/10) )

x-((6-2*449^(1/2))/10) = 0 // + (6-2*449^(1/2))/10

x = (6-2*449^(1/2))/10

( x-4 )

x-4 = 0 // + 4

x = 4

x in { 4} 

x in { (2*449^(1/2)+6)/10, (6-2*449^(1/2))/10 }

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