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On rationalizing the denominator of $\frac{1}{\sqrt{7} -\sqrt{6}}$, we get _____.
To do: Rationalize the following
Solution:
$\frac{1}{\sqrt{7} -\sqrt{6}}$
Multiply by $\sqrt{7} +\sqrt{6}$ on numerator and denominator
=$\frac{1}{\sqrt{7} -\sqrt{6}} \times \frac{\sqrt{7} +\sqrt{6}}{\sqrt{7} +\sqrt{6}}$
=$\frac{\sqrt{7} +\sqrt{6}}{\sqrt{7}^{2} -\sqrt{6}^{2}}$
=$\frac{\sqrt{7} +\sqrt{6}}{7-6}$
=$\frac{\sqrt{7} +\sqrt{6}}{1}$
=$\sqrt{7} +\sqrt{6}$
Therefore on rationalizing $\frac{1}{\sqrt{7} -\sqrt{6}}$ we get $\sqrt{7}+\sqrt{6}$
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