Question

3+√7/3-√7 racionalizar os denominadores e simplifique se possível

Answer 1

$\frac{3+ \sqrt{7} }{3- \sqrt{7} } = \\ \\ \frac{3+ \sqrt{7} }{3- \sqrt{7} }* \frac{3+ \sqrt{7}}{3+ \sqrt{7}} = \\ \\ \frac{(3+ \sqrt{7})*(3+ \sqrt{7})}{3^2- (\sqrt{7})^2 } = \\ \\ \frac{3*3+3* \sqrt{7}+ \sqrt{7} *3+\sqrt{7}* \sqrt{7} }{9-7} = \\ \\ \frac{9+3 \sqrt{7}+3 \sqrt{7} + \sqrt{49} }{2}= \\ \\ \frac{9+7+6 \sqrt{7} }{2} = \\ \\ \frac{16+6 \sqrt{7} }{2} = \\ \\ \frac{\not2\ (8+3 \sqrt{7}) }{\not2} = \\ \\ \boxed{\boxed{ 8+3 \sqrt{7} }}$