\frac{(3 + \sqrt{7})(1 + \sqrt{7})}{3(1 - 7)} = \frac{3(1) + 3\sqrt{7} + \sqrt{7} + 7}{3(-6)} = \frac{10 + 4\sqrt{7}}{-18} = -\frac{10 + 4\sqrt{7}}{18} = -\frac{5 + 2\sqrt{7}}{9}.