Question

Simplify: (3+ Root of 7) / (3-4 multiplied by root of 7) X (3+ Root of 7) / (3-4 multiplied by root of 7)

Answer 1

$$\begin{gathered} \frac{\left(3+\sqrt{7}\right)}{\left(3-4\sqrt{7}\right)}\times \frac{\left(3+\sqrt{7}\right)}{\left(3+4\sqrt{7}\right)} \\ =\frac{\left(3+\sqrt{7}\right)\left(3+\sqrt{7}\right)}{\left(3-4\sqrt{7}\right)\left(3+4\sqrt{7}\right)} \\ =\frac{{\left(3\right)}^2+{\left(\sqrt{7}\right)}^2+2\left(3\right)\left(\sqrt{7}\right)}{{\left(3\right)}^2-{\left(4\sqrt{7}\right)}^2} \\ =\frac{9+7+6\sqrt{7}}{9-112} \\ =\frac{16+6\sqrt{7}}{-103} \\ =\frac{-\left(16+6\sqrt{7}\right)}{103} \end{gathered}$$