4/(x+4)-1/(x-6)=2x/(x^2-16)

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Solution for 4/(x+4)-1/(x-6)=2x/(x^2-16) equation: 


D( x )

x-6 = 0

x^2-16 = 0

x+4 = 0

x-6 = 0

x-6 = 0

x-6 = 0 // + 6

x = 6

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+4 = 0

x+4 = 0

x+4 = 0 // - 4

x = -4

x in (-oo:-4) U (-4:4) U (4:6) U (6:+oo)

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

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

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

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

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

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

3*x^3-2*x^3-28*x^2+4*x^2-48*x+48*x+448 = 0

x^3-24*x^2+448 = 0

x^3-24*x^2+448 = 0

x^3-24*x^2+448 = 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, 224, -224, 448, -448 }

1

x = 1

x^3-24*x^2+448 = 425

1

-1

x = -1

x^3-24*x^2+448 = 423

-1

2

x = 2

x^3-24*x^2+448 = 360

2

-2

x = -2

x^3-24*x^2+448 = 344

-2

4

x = 4

x^3-24*x^2+448 = 128

4

-4

x = -4

x^3-24*x^2+448 = 0

-4

x+4

x^2-28*x+112

x^3-24*x^2+448

x+4

-x^3-4*x^2

448-28*x^2

28*x^2+112*x

112*x+448

-112*x-448

0

x^2-28*x+112 = 0

DELTA = (-28)^2-(1*4*112)

DELTA = 336

DELTA > 0

x = (336^(1/2)+28)/(1*2) or x = (28-336^(1/2))/(1*2)

x = (4*21^(1/2)+28)/2 or x = (28-4*21^(1/2))/2

x in { (28-4*21^(1/2))/2, (4*21^(1/2)+28)/2, -4} 

(x-((28-4*21^(1/2))/2))*(x-((4*21^(1/2)+28)/2))*(x+4) = 0

((x-((28-4*21^(1/2))/2))*(x-((4*21^(1/2)+28)/2))*(x+4))/((x+4)*(x-6)*(x^2-16)) = 0

((x-((28-4*21^(1/2))/2))*(x-((4*21^(1/2)+28)/2))*(x+4))/((x+4)*(x-6)*(x^2-16)) = 0 // * (x+4)*(x-6)*(x^2-16)

(x-((28-4*21^(1/2))/2))*(x-((4*21^(1/2)+28)/2))*(x+4) = 0

( x+4 )

x+4 = 0 // - 4

x = -4

( x-((28-4*21^(1/2))/2) )

x-((28-4*21^(1/2))/2) = 0 // + (28-4*21^(1/2))/2

x = (28-4*21^(1/2))/2

( x-((4*21^(1/2)+28)/2) )

x-((4*21^(1/2)+28)/2) = 0 // + (4*21^(1/2)+28)/2

x = (4*21^(1/2)+28)/2

x in { -4} 

x in { (28-4*21^(1/2))/2, (4*21^(1/2)+28)/2 }

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