(8x)/(x-3)-(24)/(x+3)=(144)/(x^2-9)

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Solution for (8x)/(x-3)-(24)/(x+3)=(144)/(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)

(8*x)/(x-3)-(24/(x+3)) = 144/(x^2-9) // - 144/(x^2-9)

(8*x)/(x-3)-(24/(x+3))-(144/(x^2-9)) = 0

(8*x)/(x-3)-24*(x+3)^-1-144*(x^2-9)^-1 = 0

(8*x)/(x-3)-24/(x+3)-144/(x^2-9) = 0

(8*x*(x+3)*(x^2-9))/((x-3)*(x+3)*(x^2-9))+(-24*(x-3)*(x^2-9))/((x-3)*(x+3)*(x^2-9))+(-144*(x-3)*(x+3))/((x-3)*(x+3)*(x^2-9)) = 0

8*x*(x+3)*(x^2-9)-24*(x-3)*(x^2-9)-144*(x-3)*(x+3) = 0

8*x^4-144*x^2-648+1296 = 0

8*x^4-144*x^2+648 = 0

8*x^4-144*x^2+648 = 0

8*(x^4-18*x^2+81) = 0

x^4-18*x^2+81 = 0

{ 1, -1, 3, -3, 9, -9, 27, -27, 81, -81 }

1

x = 1

x^4-18*x^2+81 = 64

1

-1

x = -1

x^4-18*x^2+81 = 64

-1

3

x = 3

x^4-18*x^2+81 = 0

3

x-3

x^3+3*x^2-9*x-27

x^4-18*x^2+81

x-3

3*x^3-x^4

3*x^3-18*x^2+81

9*x^2-3*x^3

81-9*x^2

9*x^2-27*x

81-27*x

27*x-81

0

x^3+3*x^2-9*x-27 = 0

{ 1, -1, 3, -3, 9, -9, 27, -27 }

1

x = 1

x^3+3*x^2-9*x-27 = -32

1

-1

x = -1

x^3+3*x^2-9*x-27 = -16

-1

3

x = 3

x^3+3*x^2-9*x-27 = 0

3

x-3

x^2+6*x+9

x^3+3*x^2-9*x-27

x-3

3*x^2-x^3

6*x^2-9*x-27

18*x-6*x^2

9*x-27

27-9*x

0

x^2+6*x+9 = 0

DELTA = 6^2-(1*4*9)

DELTA = 0

x = -6/(1*2)

x = -3 or x = -3

x in { -3, -3, 3, 3} 

8*(x+3)^2*(x-3)^2 = 0

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

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

8*(x+3)^2*(x-3)^2 = 0

( x+3 )

x+3 = 0 // - 3

x = -3

( x-3 )

x-3 = 0 // + 3

x = 3

x in { -3} 

x in { 3} 

x belongs to the empty set

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