\begin{tabular}{|l}\hline\( \square \) Question 16 \\ Determine the most simplified version of \\ the expression below: \\ \( \frac{12}{9-\sqrt{6}} \) \\ (Example: \( \frac{7-3 \sqrt{6}}{10} \) would be typed in as \\ \( 7+-3 \mathrm{rad} / 10 \) ) \\ \( \square+\square \) \\ \( \square \)\end{tabular}

To simplify the expression \( \frac{12}{9-\sqrt{6}} \), we need to rationalize the denominator. We do this by multiplying the numerator and denominator by the conjugate of the denominator, \( 9+\sqrt{6} \): \[ \frac{12(9+\sqrt{6})}{(9-\sqrt{6})(9+\sqrt{6})} \] The denominator becomes: \[ (9)^2 - (\sqrt{6})^2 = 81 - 6 = 75 \] Thus, the expression simplifies to: \[ \frac{12(9+\sqrt{6})}{75} \] This can be further simplified since \( 12/75 = 4/25 \): \[ \frac{4(9+\sqrt{6})}{25} = \frac{36 + 4\sqrt{6}}{25} \] So, in your required format, this is presented as: \( 36+ 4 \mathrm{rad} / 25 \) The final expression is: \( 36+ 4 \mathrm{rad} / 25 \)