Question

(17+12корень2/2корень2 +3) - 2корень2=?

Answer 1

$frac{17+12 sqrt{2} }{2 sqrt{2}+3 } -2 sqrt{2}= frac{17+12 sqrt{2}-2 sqrt{2}cdot 2 sqrt{2}-6 sqrt{2} }{2 sqrt{2}+3 } = frac{17+12 sqrt{2}-8-6 sqrt{2} }{2 sqrt{2}+3 } = \ = frac{9+6 sqrt{2} }{2 sqrt{2}+3 } =frac{3(3+2 sqrt{2}) }{2 sqrt{2}+3 } =3$