\text { Let us study the function } f(x)=\frac{x^{2}-4}{x^{2}-1} \text { . } A) Find the domain of the function. B) Find all asymptotes, intercepts, symmetries. C) Find the first and second derivatives. D) Find all critical points and potential inflection points. E) Study the function and its derivatives over its whole domain using the table of signs learned. F) Sketch the function to the best of your abilities, based on all details you found in this question so far.

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