The relationship between \(u\), \(v\), and \(w\) can be found by first understanding that \(w\) varies inversely with \(\frac{uv}{u + v}\), which can be represented as \(w \propto \frac{1}{uv} \cdot \frac{1}{u + v}\).

Using the constant of variation \(k\), we can write \(w = \frac{k}{uv(u + v)}\). Substituting \(u = 2\) and \(v = 6\) when \(w = 8\), we can solve for \(k\):

\[8 = \frac{k}{2 \cdot 6(2 + 6)}\]

Solving for \(k\), we get \(k = 12\).

So, the relationship is \(12(u + v) = uvw\).