(1/(x-1))+(1/(x+1))=(5/12)

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Solution for (1/(x-1))+(1/(x+1))=(5/12) equation: 


D( x )

x+1 = 0

x-1 = 0

x+1 = 0

x+1 = 0

x+1 = 0 // - 1

x = -1

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

x in (-oo:-1) U (-1:1) U (1:+oo)

1/(x-1)+1/(x+1) = 5/12 // - 5/12

1/(x-1)+1/(x+1)-(5/12) = 0

1/(x-1)+1/(x+1)-5/12 = 0

(1*12*(x+1))/(12*(x-1)*(x+1))+(1*12*(x-1))/(12*(x-1)*(x+1))+(-5*(x-1)*(x+1))/(12*(x-1)*(x+1)) = 0

1*12*(x+1)+1*12*(x-1)-5*(x-1)*(x+1) = 0

24*x-5*x^2+5 = 0

24*x-5*x^2+5 = 0

24*x-5*x^2+5 = 0

DELTA = 24^2-(-5*4*5)

DELTA = 676

DELTA > 0

x = (676^(1/2)-24)/(-5*2) or x = (-676^(1/2)-24)/(-5*2)

x = -1/5 or x = 5

(x+1/5)*(x-5) = 0

((x+1/5)*(x-5))/(12*(x-1)*(x+1)) = 0

((x+1/5)*(x-5))/(12*(x-1)*(x+1)) = 0 // * 12*(x-1)*(x+1)

(x+1/5)*(x-5) = 0

( x+1/5 )

x+1/5 = 0 // - 1/5

x = -1/5

( x-5 )

x-5 = 0 // + 5

x = 5

x in { -1/5, 5 }

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