For this case we have the following expression:
[tex]3 + 2 \sqrt {2} + \frac {1} {3 + 2 \sqrt {2}} =[/tex]
We rationalize the second term multiplying by:
[tex]\frac {3-2 \sqrt {2}} {3-2 \sqrt {2}}:[/tex][tex]\frac {1} {3 + 2 \sqrt {2}} * \frac {3-2 \sqrt {2}} {3-2 \sqrt {2}} = \frac {3-2 \sqrt {2} } {9-6 \sqrt {2} +6 \sqrt {2} -4 (\sqrt {2}) ^ 2} = \frac {3-2 \sqrt {2}} {9-4 * 2} = \frac {3-2 \sqrt {2}} {1} = 3-2 \sqrt {2}[/tex]
So, we have:
[tex]3 + 2 \sqrt {2} + 3-2 \sqrt {2} = 3 + 3 = 6[/tex]
Answer:
6
