1/(x-1)-1/(x+1)=2/(x^2-1)

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Solution for 1/(x-1)-1/(x+1)=2/(x^2-1) equation:


D( x )

x^2-1 = 0

x+1 = 0

x-1 = 0

x^2-1 = 0

x^2-1 = 0

1*x^2 = 1 // : 1

x^2 = 1

x^2 = 1 // ^ 1/2

abs(x) = 1

x = 1 or x = -1

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)) = 2/(x^2-1) // - 2/(x^2-1)

1/(x-1)-(1/(x+1))-(2/(x^2-1)) = 0

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

1/(x-1)-1/(x+1)-2/(x^2-1) = 0

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

1*(x+1)*(x^2-1)-1*(x-1)*(x^2-1)-2*(x-1)*(x+1) = 0

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

0 = 0

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

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

0 = 0

x belongs to the empty set

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