Question

how is the answer -1/3
?

Answer 1

Rationalize the denominator. Times the top and bottom of the fraction by the conjugate of the bottom:
\[\frac{ \frac{ \sqrt{2} }{2} - \sqrt{2} }{ \frac{ \sqrt{2} }{2} + \sqrt{2} }\]

The conjugate of the bottom is:
\[\frac{ \sqrt{2} }{2} - \sqrt{2} \]

Multiply by the top and bottom by this, which is the same as multiplying by 1, so were not changing the value of the fraction:

\[\frac{ (\frac{ \sqrt{2} }{2} - \sqrt{2})(\frac{ \sqrt{2} }{2} - \sqrt{2} ) }{ (\frac{ \sqrt{2} }{2} + \sqrt{2})(\frac{ \sqrt{2} }{2} - \sqrt{2} ) }\]

You should be able to multiply out of the brackets and start to simplify your answer.

Answer 2

or, you could multiply everything by 1 or
\[\frac{\sqrt{2}}{\sqrt{2}}\]
and then simplify