((5x)/(x^2-81))/((6x-24)/(8x+72))=x

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Solution for ((5x)/(x^2-81))/((6x-24)/(8x+72))=x equation:


D( x )

8*x+72 = 0

x^2-81 = 0

(6*x-24)/(8*x+72) = 0

8*x+72 = 0

8*x+72 = 0

8*x+72 = 0 // - 72

8*x = -72 // : 8

x = -72/8

x = -9

x^2-81 = 0

x^2-81 = 0

1*x^2 = 81 // : 1

x^2 = 81

x^2 = 81 // ^ 1/2

abs(x) = 9

x = 9 or x = -9

(6*x-24)/(8*x+72) = 0

(6*x-24)/(8*x+72) = 0

6*x-24 = 0 // + 24

6*x = 24 // : 6

x = 24/6

x = 4

x in (-oo:-9) U (-9:4) U (4:9) U (9:+oo)

((5*x)/(x^2-81))/((6*x-24)/(8*x+72)) = x // - x

((5*x)/(x^2-81))/((6*x-24)/(8*x+72))-x = 0

(5*x*(8*x+72))/((x^2-81)*(6*x-24))-x = 0

(5*x*(8*x+72))/((x^2-81)*(6*x-24))+(-x*(x^2-81)*(6*x-24))/((x^2-81)*(6*x-24)) = 0

5*x*(8*x+72)-x*(x^2-81)*(6*x-24) = 0

24*x^3-6*x^4+526*x^2-1584*x = 0

24*x^3-6*x^4+526*x^2-1584*x = 0

2*x*(12*x^2-3*x^3+263*x-792) = 0

12*x^2-3*x^3+263*x-792 = 0

{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 9, -9, 11, -11, 12, -12, 18, -18, 22, -22, 24, -24, 33, -33, 36, -36, 44, -44, 66, -66, 72, -72, 88, -88, 99, -99, 132, -132, 198, -198, 264, -264, 396, -396, 792, -792 }

1

x = 1

12*x^2-3*x^3+263*x-792 = -520

1

-1

x = -1

12*x^2-3*x^3+263*x-792 = -1040

-1

2

x = 2

12*x^2-3*x^3+263*x-792 = -242

2

-2

x = -2

12*x^2-3*x^3+263*x-792 = -1246

-2

3

x = 3

12*x^2-3*x^3+263*x-792 = 24

3

-3

x = -3

12*x^2-3*x^3+263*x-792 = -1392

-3

4

x = 4

12*x^2-3*x^3+263*x-792 = 260

4

-4

x = -4

12*x^2-3*x^3+263*x-792 = -1460

-4

6

x = 6

12*x^2-3*x^3+263*x-792 = 570

6

-6

x = -6

12*x^2-3*x^3+263*x-792 = -1290

-6

8

x = 8

12*x^2-3*x^3+263*x-792 = 544

8

-8

x = -8

12*x^2-3*x^3+263*x-792 = -592

-8

9

x = 9

12*x^2-3*x^3+263*x-792 = 360

9

-9

x = -9

12*x^2-3*x^3+263*x-792 = 0

-9

x+9

39*x-3*x^2-88

12*x^2-3*x^3+263*x-792

x+9

3*x^3+27*x^2

39*x^2+263*x-792

-39*x^2-351*x

-88*x-792

88*x+792

0

39*x-3*x^2-88 = 0

DELTA = 39^2-(-88*(-3)*4)

DELTA = 465

DELTA > 0

x = (465^(1/2)-39)/(-3*2) or x = (-465^(1/2)-39)/(-3*2)

x = (465^(1/2)-39)/(-6) or x = (465^(1/2)+39)/6

x in { (465^(1/2)-39)/(-6), (465^(1/2)+39)/6, -9}

2*x*(x-((465^(1/2)-39)/(-6)))*(x-((465^(1/2)+39)/6))*(x+9) = 0

(2*x*(x-((465^(1/2)-39)/(-6)))*(x-((465^(1/2)+39)/6))*(x+9))/((x^2-81)*(6*x-24)) = 0

(2*x*(x-((465^(1/2)-39)/(-6)))*(x-((465^(1/2)+39)/6))*(x+9))/((x^2-81)*(6*x-24)) = 0 // * (x^2-81)*(6*x-24)

2*x*(x-((465^(1/2)-39)/(-6)))*(x-((465^(1/2)+39)/6))*(x+9) = 0

( 2*x )

2*x = 0 // : 2

x = 0

( x+9 )

x+9 = 0 // - 9

x = -9

( x-((465^(1/2)+39)/6) )

x-((465^(1/2)+39)/6) = 0 // + (465^(1/2)+39)/6

x = (465^(1/2)+39)/6

( x-((465^(1/2)-39)/(-6)) )

x-((465^(1/2)-39)/(-6)) = 0 // + (465^(1/2)-39)/(-6)

x = (465^(1/2)-39)/(-6)

x in { -9}

x in { 0, (465^(1/2)+39)/6, (465^(1/2)-39)/(-6) }

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