Is this book answer wrong?

Question

I came across this simplification exercise which tells us to simplify: $\frac{\sqrt{8} - \sqrt{16}}{4 - \sqrt{2}} - 2^{1/2}$.

The answer in the book is $\frac{-5\sqrt{2} -6}{7}$.

I'm getting close but not to this answer, wondering if it's correct.

Thanks in advance, I tried alot of resources to solve this, maybe someone knows what's up.

Answer 1

$$ \frac{2\sqrt{2}-4}{4-\sqrt{2}}-\sqrt{2}=\\ \frac{2\sqrt{2}-4}{4-\sqrt{2}}\cdot \frac{4+\sqrt{2}}{4+\sqrt{2}}-\sqrt{2}=\\ \frac{8\sqrt{2}-16+4-4\sqrt{2}}{16-2}-\sqrt{2}=\\ \frac{4\sqrt{2}-12}{14}-\sqrt{2}=\\ \frac{2\sqrt{2}-6}{7}-\sqrt{2}=\\ \frac{2\sqrt{2}-6-7\sqrt{2}}{7}=\\ \frac{-5\sqrt{2}-6}{7} $$