1/(x-3)+1/(x+3)=12/(x^2-9)

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Solution for 1/(x-3)+1/(x+3)=12/(x^2-9) equation: 


D( x )

x-3 = 0

x^2-9 = 0

x+3 = 0

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

x^2-9 = 0

x^2-9 = 0

1*x^2 = 9 // : 1

x^2 = 9

x^2 = 9 // ^ 1/2

abs(x) = 3

x = 3 or x = -3

x+3 = 0

x+3 = 0

x+3 = 0 // - 3

x = -3

x in (-oo:-3) U (-3:3) U (3:+oo)

1/(x-3)+1/(x+3) = 12/(x^2-9) // - 12/(x^2-9)

1/(x-3)+1/(x+3)-(12/(x^2-9)) = 0

1/(x-3)+1/(x+3)-12*(x^2-9)^-1 = 0

1/(x-3)+1/(x+3)-12/(x^2-9) = 0

(1*(x+3)*(x^2-9))/((x-3)*(x+3)*(x^2-9))+(1*(x-3)*(x^2-9))/((x-3)*(x+3)*(x^2-9))+(-12*(x-3)*(x+3))/((x-3)*(x+3)*(x^2-9)) = 0

1*(x+3)*(x^2-9)+1*(x-3)*(x^2-9)-12*(x-3)*(x+3) = 0

2*x^3-12*x^2-18*x+108 = 0

2*x^3-12*x^2-18*x+108 = 0

2*(x^3-6*x^2-9*x+54) = 0

x^3-6*x^2-9*x+54 = 0

{ 1, -1, 2, -2, 3, -3, 6, -6, 9, -9, 18, -18, 27, -27, 54, -54 }

1

x = 1

x^3-6*x^2-9*x+54 = 40

1

-1

x = -1

x^3-6*x^2-9*x+54 = 56

-1

2

x = 2

x^3-6*x^2-9*x+54 = 20

2

-2

x = -2

x^3-6*x^2-9*x+54 = 40

-2

3

x = 3

x^3-6*x^2-9*x+54 = 0

3

x-3

x^2-3*x-18

x^3-6*x^2-9*x+54

x-3

3*x^2-x^3

54-3*x^2-9*x

3*x^2-9*x

54-18*x

18*x-54

0

x^2-3*x-18 = 0

DELTA = (-3)^2-(-18*1*4)

DELTA = 81

DELTA > 0

x = (81^(1/2)+3)/(1*2) or x = (3-81^(1/2))/(1*2)

x = 6 or x = -3

x in { -3, 6, 3} 

2*(x+3)*(x-6)*(x-3) = 0

(2*(x+3)*(x-6)*(x-3))/((x-3)*(x+3)*(x^2-9)) = 0

(2*(x+3)*(x-6)*(x-3))/((x-3)*(x+3)*(x^2-9)) = 0 // * (x-3)*(x+3)*(x^2-9)

2*(x+3)*(x-6)*(x-3) = 0

( x+3 )

x+3 = 0 // - 3

x = -3

( x-3 )

x-3 = 0 // + 3

x = 3

( x-6 )

x-6 = 0 // + 6

x = 6

x in { -3} 

x in { 3} 

x = 6

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