Right choice is (b) \(\frac{5-\sqrt{7}}{18}\)
Explanation: When the denominator of an expression contains a term with a square root, the process of converting it to an equivalent expression whose denominator is a rational number is called rationalising the denominator.
By multiplying \(\frac{1}{5+\sqrt{7}}\) by \(5-\sqrt{7}\), we will get same expression since \(\frac{5-\sqrt{7}}{5-\sqrt{7}}\) = 1.
Therefore, \(\frac{1}{5+\sqrt{7}} = {\frac{1}{5+\sqrt{7}}} * (\frac{5-\sqrt{7}}{5-\sqrt{7}})\)
= \(\frac{5-\sqrt{7}}{(5*5)-(\sqrt{7}*\sqrt{7})}\)
= \(\frac{5-\sqrt{7}}{25-7}\)
= \(\frac{5-\sqrt{7}}{18}\).