- Given that \(x > 0\), \(y > 0\), \(z > 0\) and that \(x + y + z = 3\), prove that \[\begin{equation*} \frac{1}{x} + \frac{1}{y} + \frac{1}{z} \ge 3. \end{equation*}\]

We know from the first part of the question that if \(a > 0\) and \(b > 0\), then
\[\begin{equation*}
\frac{a}{b} + \frac{b}{a} \ge 2.
\end{equation*}\]

How could we make this look more like the fractions in part (ii)?