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

[latex] \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[/latex]