Systems of Equations · Challenge problem

For every pair of numbers $x$ and $y$ with $x + y = g$ and $xy = h$, express each of the following in terms of $g$ and $h$ alone.

$(a)\ \dfrac{1}{x} + \dfrac{1}{y}$ $(b)\ x^3 + y^3$ $(c)\ (x-y)^2$