The function is $\displaystyle f(x) = \frac{x^2}{x^2 - 1}$ The answer key claims there to be no points of inflection, yet I found from my second derivative

$\displaystyle f''(x) = \frac{-10x^2 + 2}{(x^2 - 1)^3}$ I find the points $\displaystyle x = \pm\sqrt{\frac{1}{5}}$ Could it be possible that the answer key is wrong?