Evaluate
\frac{\sqrt{2}+3}{7}\approx 0.630601937
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\frac{3+\sqrt{2}}{\left(3-\sqrt{2}\right)\left(3+\sqrt{2}\right)}
Rationalize the denominator of \frac{1}{3-\sqrt{2}} by multiplying numerator and denominator by 3+\sqrt{2}.
\frac{3+\sqrt{2}}{3^{2}-\left(\sqrt{2}\right)^{2}}
Consider \left(3-\sqrt{2}\right)\left(3+\sqrt{2}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\frac{3+\sqrt{2}}{9-2}
Square 3. Square \sqrt{2}.
\frac{3+\sqrt{2}}{7}
Subtract 2 from 9 to get 7.
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