Question

If $x=\sqrt{2}+\sqrt{3}$ find $\frac{x^2+1}{x^2-2}$.

Answer 1

$x=\sqrt{2}+\sqrt{3}$

$x^2=2+3+2\sqrt{6}$

$x^2=5+2\sqrt{6}$

$\frac{x^2+1}{x^2-1}=\frac{5+2\sqrt{6}+1}{5+2\sqrt{6}-1}$

$=\frac{2\sqrt{6}+6}{2\sqrt{6}+4}$