Hi Stephen,

I would work with the numerator first,

\[(1+x)^{1/3} -1/3 x (1+x)^{-2/3} = (1+x)^{1/3} - \frac{1/3 x}{(1+x)^{2/3}}.\]

Express these two terms with the common denominator $(1+x)^{2/3}$ and simplify. Now reintroduce the original denominator by multiplying the simplified numerator by

\[\frac{1}{(1+x)^{2/3}}.\]

Penny