Answer
a)$\frac{1}{1-t}$, $-\frac{1}{t}$
b) $x=\frac{3}{2}$
Work Step by Step
a)
(i) $$
\frac{\frac{1}{t}}{\frac{1}{t}-1}=\frac{\frac{1}{t}}{\frac{1-t}{t}}=\frac{1}{t} \cdot \frac{t}{1-t}=\frac{1}{1-t} .
$$
ii) $$
\frac{\frac{1}{t+1}}{\frac{1}{t+1}-1}=\frac{1}{t+1} \cdot \frac{t+1}{1-t-1}=-\frac{1}{t}
$$
b) Solve $f(x)=\frac{x}{(x-1)}=3$, so
$$
\begin{aligned}
& x=3 x-3 \\
& 3=2 x \\
& x=\frac{3}{2} .
\end{aligned}
$$
