If N = frac{sqrt{6} - sqrt{5}}{sqrt{6} + sqrt | vedclass

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(D) Given $N = \frac{\sqrt{6} - \sqrt{5}}{\sqrt{6} + \sqrt{5}}$.First,rationalize the denominator of $N$:$N = \frac{(\sqrt{6} - \sqrt{5})(\sqrt{6} - \

Vedclass · Accepted Answer

$22$

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(D) Given $N = \frac{\sqrt{6} - \sqrt{5}}{\sqrt{6} + \sqrt{5}}$.First,rationalize the denominator of $N$:$N = \frac{(\sqrt{6} - \sqrt{5})(\sqrt{6} - \sqrt{5})}{(\sqrt{6} + \sqrt{5})(\sqrt{6} - \sqrt{5})} = \frac{(\sqrt{6} - \sqrt{5})^2}{6 - 5} = 6 + 5 - 2\sqrt{30} = 11 - 2\sqrt{30}$.Now,find $\frac{1}{N}$:$\frac{1}{N} = \frac{1}{11 - 2\sqrt{30}}$.Rationalize the denominator of $\frac{1}{N}$:$\frac{1}{N} = \frac{11 + 2\sqrt{30}}{(11 - 2\sqrt{30})(11 + 2\sqrt{30})} = \frac{11 + 2\sqrt{30}}{121 - (4 	imes 30)} = \frac{11 + 2\sqrt{30}}{121 - 120} = 11 + 2\sqrt{30}$.Finally,calculate $N + \frac{1}{N}$:$N + \frac{1}{N} = (11 - 2\sqrt{30}) + (11 + 2\sqrt{30}) = 11 + 11 = 22$.

If $N = \frac{\sqrt{6} - \sqrt{5}}{\sqrt{6} + \sqrt{5}},$ then what is the value of $N + \frac{1}{N} ?$

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