simplify the equation [1/(x-1)-1/(x+1)+1]*(x+1)/(x^2+1)

We'll multiply by LCD inside the first pair of
brackets:

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

[(x+1-x+1+x^2-1)/(x^2-1)]*[(x+1)/(x^2+1)]

We'll
combine and eliminate like terms:

[(x^2 +
1)/(x^2-1)]*[(x+1)/(x^2+1)]

We'll simplify by
(x^2+1):

[(x^2 + 1)/(x^2-1)]*[(x+1)/(x^2+1)] =
(x+1)/(x^2-1)

W'll re-write the difference of squares from
denominator as a product:

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

We'll simplify by
(x+1):

E(x) =
1/(x-1)

The simplified expression is E(x) =
1/(x-1).