Question

$frac{6-4 sqrt{2} }{ sqrt{2} -1} -2 sqrt{2}$

Answer 1

$displaystyle frac{6-4 sqrt{2} }{sqrt{2}-1}-2sqrt{2}= frac{6-4sqrt{2}}{sqrt{2}-1} - frac{2sqrt{2}(sqrt{2}-1)}{sqrt{2}-1}=\ \ \ = frac{6-4sqrt{2}-4+2sqrt{2}}{sqrt{2}-1}= frac{2-2sqrt{2}}{sqrt{2}-1} = -frac{2(sqrt{2}-1)}{sqrt{2}-1}= -2$