Question

Express 1/(1+√2 - √3) with rational denominator

Answer 1

$\dfrac{1}{1+ \sqrt{2} - \sqrt{3} }$

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

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

$=\dfrac{1+ \sqrt{2} + \sqrt{3}}{1^2+ 2\sqrt{2} + \sqrt{2}^2 - 3}$

$= \dfrac{1+ \sqrt{2} + \sqrt{3}}{1+ 2\sqrt{2} +2 - 3}$

$= \dfrac{1+ \sqrt{2} + \sqrt{3}}{2\sqrt{2}}$

$= \dfrac{1+ \sqrt{2} + \sqrt{3}}{2\sqrt{2}} \times \dfrac{\sqrt{2}} {\sqrt{2}}$

$= \dfrac{\sqrt{2} (1+ \sqrt{2} + \sqrt{3})}{4}$

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

Answer 2

here is your answer!!!!

hope you are able to understand!!!!