Evaluate
\frac{\sqrt{7}+5}{18}\approx 0.424763962
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\frac{5+\sqrt{7}}{\left(5-\sqrt{7}\right)\left(5+\sqrt{7}\right)}
Rationalize the denominator of \frac{1}{5-\sqrt{7}} by multiplying numerator and denominator by 5+\sqrt{7}.
\frac{5+\sqrt{7}}{5^{2}-\left(\sqrt{7}\right)^{2}}
Consider \left(5-\sqrt{7}\right)\left(5+\sqrt{7}\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{5+\sqrt{7}}{25-7}
Square 5. Square \sqrt{7}.
\frac{5+\sqrt{7}}{18}
Subtract 7 from 25 to get 18.
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