Surds

[Tanuja Nair]

Express 1÷(1+√2 - √3) as an equivalent fraction with a rational denominator

[Saumik Karfa]

$\frac {1}{(1+\sqrt 2)-\sqrt 3}$

$= \frac {(1+\sqrt 2)+\sqrt 3}{(1+\sqrt 2)^2-3}$

$= \frac {(1+\sqrt 2)+\sqrt 3}{1+2\sqrt 2+2-3}$

$= \frac{(1+\sqrt 2)+\sqrt 3}{2\sqrt 2} \times \frac {\sqrt 2}{\sqrt 2}$

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

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