(x/(x-2))+(x/(x+2))=(50/(x^2-4))

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Solution for (x/(x-2))+(x/(x+2))=(50/(x^2-4)) equation: 


D( x )

x+2 = 0

x-2 = 0

x^2-4 = 0

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x^2-4 = 0

x^2-4 = 0

1*x^2 = 4 // : 1

x^2 = 4

x^2 = 4 // ^ 1/2

abs(x) = 2

x = 2 or x = -2

x in (-oo:-2) U (-2:2) U (2:+oo)

x/(x-2)+x/(x+2) = 50/(x^2-4) // - 50/(x^2-4)

x/(x-2)+x/(x+2)-(50/(x^2-4)) = 0

x/(x-2)+x/(x+2)-50*(x^2-4)^-1 = 0

x/(x-2)+x/(x+2)-50/(x^2-4) = 0

(x*(x+2)*(x^2-4))/((x-2)*(x+2)*(x^2-4))+(x*(x-2)*(x^2-4))/((x-2)*(x+2)*(x^2-4))+(-50*(x-2)*(x+2))/((x-2)*(x+2)*(x^2-4)) = 0

x*(x+2)*(x^2-4)+x*(x-2)*(x^2-4)-50*(x-2)*(x+2) = 0

2*x^4-8*x^2-50*x^2+200 = 0

2*x^4-58*x^2+200 = 0

2*x^4-58*x^2+200 = 0

2*(x^4-29*x^2+100) = 0

x^4-29*x^2+100 = 0

{ 1, -1, 2, -2, 4, -4, 5, -5, 10, -10, 20, -20, 25, -25, 50, -50, 100, -100 }

1

x = 1

x^4-29*x^2+100 = 72

1

-1

x = -1

x^4-29*x^2+100 = 72

-1

2

x = 2

x^4-29*x^2+100 = 0

2

x-2

x^3+2*x^2-25*x-50

x^4-29*x^2+100

x-2

2*x^3-x^4

2*x^3-29*x^2+100

4*x^2-2*x^3

100-25*x^2

25*x^2-50*x

100-50*x

50*x-100

0

x^3+2*x^2-25*x-50 = 0

{ 1, -1, 2, -2, 5, -5, 10, -10, 25, -25, 50, -50 }

1

x = 1

x^3+2*x^2-25*x-50 = -72

1

-1

x = -1

x^3+2*x^2-25*x-50 = -24

-1

2

x = 2

x^3+2*x^2-25*x-50 = -84

2

-2

x = -2

x^3+2*x^2-25*x-50 = 0

-2

x+2

x^2-25

x^3+2*x^2-25*x-50

x+2

-x^3-2*x^2

-25*x-50

25*x+50

0

x^2-25 = 0

DELTA = 0^2-(-25*1*4)

DELTA = 100

DELTA > 0

x = (100^(1/2)+0)/(1*2) or x = (0-100^(1/2))/(1*2)

x = 5 or x = -5

x in { -5, 5, 2, -2} 

2*(x+5)*(x-5)*(x-2)*(x+2) = 0

(2*(x+5)*(x-5)*(x-2)*(x+2))/((x-2)*(x+2)*(x^2-4)) = 0

(2*(x+5)*(x-5)*(x-2)*(x+2))/((x-2)*(x+2)*(x^2-4)) = 0 // * (x-2)*(x+2)*(x^2-4)

2*(x+5)*(x-5)*(x-2)*(x+2) = 0

( x+2 )

x+2 = 0 // - 2

x = -2

( x+5 )

x+5 = 0 // - 5

x = -5

( x-2 )

x-2 = 0 // + 2

x = 2

( x-5 )

x-5 = 0 // + 5

x = 5

x in { -2} 

x in { 2} 

x in { -5, 5 }

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