Simplify \(( \sqrt { } ( 1 + x ) + \sqrt { } ( 1 - x ) ) ( \sqrt { } ( 1 + x ) - \sqrt { } ( 1 - x ) )\), showing your working, and deduce that
$$\frac { 1 } { \sqrt { } ( 1 + x ) + \sqrt { } ( 1 - x ) } = \frac { \sqrt { } ( 1 + x ) - \sqrt { } ( 1 - x ) } { 2 x }$$
Using this result, or otherwise, obtain the expansion of
$$\frac { 1 } { \sqrt { } ( 1 + x ) + \sqrt { } ( 1 - x ) }$$
in ascending powers of \(x\), up to and including the term in \(x ^ { 2 }\).