(3/(x^2-36))=(2/(x-6))-(5/(x+6))

Solution for (3/(x^2-36))=(2/(x-6))-(5/(x+6)) equation:

D( x )

x-6 = 0

x^2-36 = 0

x+6 = 0

x-6 = 0

x-6 = 0

x-6 = 0 // + 6

x = 6

x^2-36 = 0

x^2-36 = 0

1*x^2 = 36 // : 1

x^2 = 36

x^2 = 36 // ^ 1/2

abs(x) = 6

x = 6 or x = -6

x+6 = 0

x+6 = 0

x+6 = 0 // - 6

x = -6

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

3/(x^2-36) = 2/(x-6)-(5/(x+6)) // - 2/(x-6)-(5/(x+6))

3/(x^2-36)-(2/(x-6))+5/(x+6) = 0

3/(x^2-36)-2*(x-6)^-1+5/(x+6) = 0

3/(x^2-36)-2/(x-6)+5/(x+6) = 0

(3*(x-6)*(x+6))/((x^2-36)*(x-6)*(x+6))+(-2*(x^2-36)*(x+6))/((x^2-36)*(x-6)*(x+6))+(5*(x^2-36)*(x-6))/((x^2-36)*(x-6)*(x+6)) = 0

3*(x-6)*(x+6)-2*(x^2-36)*(x+6)+5*(x^2-36)*(x-6) = 0

5*x^3-2*x^3-9*x^2-30*x^2+72*x-180*x+324+1080 = 0

3*x^3-39*x^2-108*x+1404 = 0

3*x^3-39*x^2-108*x+1404 = 0

3*(x^3-13*x^2-36*x+468) = 0

x^3-13*x^2-36*x+468 = 0

{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 9, -9, 12, -12, 13, -13, 18, -18, 26, -26, 36, -36, 39, -39, 52, -52, 78, -78, 117, -117, 156, -156, 234, -234, 468, -468 }

1

x = 1

x^3-13*x^2-36*x+468 = 420

1

-1

x = -1

x^3-13*x^2-36*x+468 = 490

-1

2

x = 2

x^3-13*x^2-36*x+468 = 352

2

-2

x = -2

x^3-13*x^2-36*x+468 = 480

-2

3

x = 3

x^3-13*x^2-36*x+468 = 270

3

-3

x = -3

x^3-13*x^2-36*x+468 = 432

-3

4

x = 4

x^3-13*x^2-36*x+468 = 180

4

-4

x = -4

x^3-13*x^2-36*x+468 = 340

-4

6

x = 6

x^3-13*x^2-36*x+468 = 0

6

x-6

x^2-7*x-78

x^3-13*x^2-36*x+468

x-6

6*x^2-x^3

468-7*x^2-36*x

7*x^2-42*x

468-78*x

78*x-468

0

x^2-7*x-78 = 0

DELTA = (-7)^2-(-78*1*4)

DELTA = 361

DELTA > 0

x = (361^(1/2)+7)/(1*2) or x = (7-361^(1/2))/(1*2)

x = 13 or x = -6

x in { -6, 13, 6} 

3*(x+6)*(x-13)*(x-6) = 0

(3*(x+6)*(x-13)*(x-6))/((x^2-36)*(x-6)*(x+6)) = 0

(3*(x+6)*(x-13)*(x-6))/((x^2-36)*(x-6)*(x+6)) = 0 // * (x^2-36)*(x-6)*(x+6)

3*(x+6)*(x-13)*(x-6) = 0

( x+6 )

x+6 = 0 // - 6

x = -6

( x-13 )

x-13 = 0 // + 13

x = 13

( x-6 )

x-6 = 0 // + 6

x = 6

x in { -6} 

x in { 6} 

x = 13