(x/(x-11))-(11/(x+11))=((22x)/(x^2-121))

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Solution for (x/(x-11))-(11/(x+11))=((22x)/(x^2-121)) equation: 


D( x )

x-11 = 0

x+11 = 0

x^2-121 = 0

x-11 = 0

x-11 = 0

x-11 = 0 // + 11

x = 11

x+11 = 0

x+11 = 0

x+11 = 0 // - 11

x = -11

x^2-121 = 0

x^2-121 = 0

1*x^2 = 121 // : 1

x^2 = 121

x^2 = 121 // ^ 1/2

abs(x) = 11

x = 11 or x = -11

x in (-oo:-11) U (-11:11) U (11:+oo)

x/(x-11)-(11/(x+11)) = (22*x)/(x^2-121) // - (22*x)/(x^2-121)

x/(x-11)-(11/(x+11))-((22*x)/(x^2-121)) = 0

x/(x-11)-11*(x+11)^-1-22*x*(x^2-121)^-1 = 0

x/(x-11)-11/(x+11)+(-22*x)/(x^2-121) = 0

(x*(x+11)*(x^2-121))/((x-11)*(x+11)*(x^2-121))+(-11*(x-11)*(x^2-121))/((x-11)*(x+11)*(x^2-121))+(-22*x*(x-11)*(x+11))/((x-11)*(x+11)*(x^2-121)) = 0

x*(x+11)*(x^2-121)-11*(x-11)*(x^2-121)-22*x*(x-11)*(x+11) = 0

x^4-22*x^3+2662*x-14641 = 0

x^4-22*x^3+2662*x-14641 = 0

x^4-22*x^3+2662*x-14641 = 0

{ 1, -1, 11, -11, 121, -121, 1331, -1331, 14641, -14641 }

1

x = 1

x^4-22*x^3+2662*x-14641 = -12000

1

-1

x = -1

x^4-22*x^3+2662*x-14641 = -17280

-1

11

x = 11

x^4-22*x^3+2662*x-14641 = 0

11

x-11

x^3-11*x^2-121*x+1331

x^4-22*x^3+2662*x-14641

x-11

11*x^3-x^4

2662*x-11*x^3-14641

11*x^3-121*x^2

2662*x-121*x^2-14641

121*x^2-1331*x

1331*x-14641

14641-1331*x

0

x^3-11*x^2-121*x+1331 = 0

{ 1, -1, 11, -11, 121, -121, 1331, -1331 }

1

x = 1

x^3-11*x^2-121*x+1331 = 1200

1

-1

x = -1

x^3-11*x^2-121*x+1331 = 1440

-1

11

x = 11

x^3-11*x^2-121*x+1331 = 0

11

x-11

x^2-121

x^3-11*x^2-121*x+1331

x-11

11*x^2-x^3

1331-121*x

121*x-1331

0

x^2-121 = 0

DELTA = 0^2-(-121*1*4)

DELTA = 484

DELTA > 0

x = (484^(1/2)+0)/(1*2) or x = (0-484^(1/2))/(1*2)

x = 11 or x = -11

x in { -11, 11, 11, 11} 

(x+11)*(x-11)^3 = 0

((x+11)*(x-11)^3)/((x-11)*(x+11)*(x^2-121)) = 0

((x+11)*(x-11)^3)/((x-11)*(x+11)*(x^2-121)) = 0 // * (x-11)*(x+11)*(x^2-121)

(x+11)*(x-11)^3 = 0

( x+11 )

x+11 = 0 // - 11

x = -11

( x-11 )

x-11 = 0 // + 11

x = 11

x in { -11} 

x in { 11} 

x belongs to the empty set

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