a) Para encontrarmos a função em (t), devemos realizar os cálculos abaixo:

\(\begin{align} & f(x)=\frac{{{x}^{2}}-4}{x-1} \\ & f(x)=\frac{1}{t} \\ & f(x)=\frac{{{\left( \frac{1}{t} \right)}^{2}}-4}{\frac{1}{t}-1} \\ & f(x)=\frac{\frac{1}{{{t}^{2}}}-4}{\frac{1}{t}-1} \\ & f(x)=\left( \frac{1-4{{t}^{2}}}{{{t}^{2}}} \right)\left( \frac{t}{1-t} \right) \\ & f(x)=\frac{t-4{{t}^{3}}}{{{t}^{2}}-{{t}^{3}}} \\ & f(x)=\frac{1-4{{t}^{2}}}{t-{{t}^{2}}} \\ \end{align} \)

\(\boxed{f\left( x \right) = \frac{{1 - 4{t^2}}}{{t - {t^2}}}}\)

b) Repetiremos o mesmo processo do item A:

\(\begin{align} & f(x)=\frac{{{x}^{2}}-4}{x-1} \\ & f(x)={{t}^{2}} \\ & f(x)=\frac{{{\left( {{t}^{2}} \right)}^{2}}-4}{{{t}^{2}}-1} \\ & f(x)=\frac{{{t}^{4}}-4}{{{t}^{2}}-1} \\ \end{align} \)

\(\boxed{f\left( x \right) = \frac{{{t^4} - 4}}{{{t^2} - 1}}}\)