On the 2nd page, we can save a lot of steps by using the product rule instead of quotient, with the second factor of the product being (3+x^2)^{-2}. I did wind up with the same answer!
I don't understand the last part of p. 3. The function is continuous at x=0, with
lim(x->0+) = lim(x->0-) = f(0) = 1/3.
It is also true that f(-1) = f(1) = 1/4 .. no infinities.
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