Question

simplify the question
​

Answer 1

Question -

$simplify \: \: \frac{3 - \sqrt{2} }{3 + \sqrt{2} } + \frac{3 + \sqrt{2} }{3 - \sqrt{2} }$

Solution-

$= \frac{3 - \sqrt{2} }{3 + \sqrt{2} } + \frac{3 + \sqrt{2} }{3 - \sqrt{2} }$

By rationalising the denominator we will get,

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

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

$= \frac{ {(3)}^{2} + {( \sqrt{2}) }^{2} - 2 \times 3 \times \sqrt{2} }{9 - 2} + \frac{ {(3)}^{2} + ({ \sqrt{2} )}^{2} + 2 \times 3 \times \sqrt{2} }{9 - 2}$

$= \frac{9 + 2 - 6 \sqrt{2} }{7} + \frac{9 + 2 + 6 \sqrt{2} }{7}$

$= \frac{11 - 6 \sqrt{2} }{7} + \frac{11 + 6 \sqrt{2} }{7}$

By taking L. C. M,

$= \frac{11 - 6 \sqrt{2} + 11 + 6 \sqrt{2} }{7}$

$= \frac{22}{7}$