If $mathrm{N}=frac{(sqrt{6}-sqrt{5})}{(sqrt{6}+sqrt{5})}$, then what is the value of $mathrm{N}+$

$left(frac{1}{N} ight) ?$

$mathrm{N}=frac{sqrt{6}-sqrt{5}}{sqrt{6}+sqrt{5}}=frac{sqrt{6}-sqrt{5}}{sqrt{6}+sqrt{5}} imes frac{sqrt{6}-sqrt{5}}{sqrt{6}-sqrt{5}}$

$=frac{(sqrt{6}-sqrt{5})^{2}}{(sqrt{6})^{2}-(sqrt{5})^{2}}=frac{6+5-2 sqrt{30}}{6-5}$

$=11-2 sqrt{30}$

$herefore frac{1}{mathrm{~N}}=11+2 sqrt{30}$

$herefore mathrm{N}+frac{1}{mathrm{~N}}=11-2 sqrt{30}+11+2 sqrt{30}=22$