Answer
$-\dfrac{1}{2-2\sqrt2}$
Work Step by Step
Rationalize the numerator by multiplying $1-\sqrt{2}$ to both the numerator and the denominator to have:
$=\dfrac{1+\sqrt{2}}{2} \cdot \dfrac{1-\sqrt{2}}{1-\sqrt{2}}
\\=\dfrac{1-2}{2-2\sqrt2}
\\=-\dfrac{1}{2-2\sqrt2}$
