\[\frac{3}{2+\sqrt{2}}\]
1
Rationalize the denominator: 32+2⋅2−22−2=6−3222−22\frac{3}{2+\sqrt{2}} \cdot \frac{2-\sqrt{2}}{2-\sqrt{2}}=\frac{6-3\sqrt{2}}{{2}^{2}-{\sqrt{2}}^{2}}.
6−3222−22\frac{6-3\sqrt{2}}{{2}^{2}-{\sqrt{2}}^{2}}

2
Factor out the common term 33.
3(2−2)22−22\frac{3(2-\sqrt{2})}{{2}^{2}-{\sqrt{2}}^{2}}

3
Simplify  22{2}^{2}  to  44.
3(2−2)4−22\frac{3(2-\sqrt{2})}{4-{\sqrt{2}}^{2}}

4
Use this rule: x2=x{\sqrt{x}}^{2}=x.
3(2−2)4−2\frac{3(2-\sqrt{2})}{4-2}

5
Simplify  4−24-2  to  22.
3(2−2)2\frac{3(2-\sqrt{2})}{2}

Done

Decimal Form: 0.878680
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