Question

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

Answer 1

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