\(\frac{5+\sqrt{7}}{3+\sqrt{7}}=\frac{5+\sqrt{7}}{3+\sqrt{7}}\times \frac{3-\sqrt{7}}{3-\sqrt{7}}\) =\(\frac{(5+\sqrt{7})(3-\sqrt{7})}{3^2 - \sqrt{7}^2}\) =\(\frac{15-5\sqrt{7}+3\sqrt{7}-7}{9-7}\) = \(\frac{8-2\sqrt{7}}{2}\) Factorize, then divide by 2 \(=\frac{2(4-\sqrt{7}}{2})\) =4-\(\sqrt{7}\)