(a) For $f(x)=\frac{x^{2}-3}{x^{2}+1}$, we can use the quotient rule for differentiation which states that the derivative of $\frac{u}{v}$ is $\frac{vu'-uv'}{v^2}$, where $u$ and $v$ are differentiable functions of $x$. Here, $u=x^2-3$ and $v=x^2+1$. The
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