Question

Please solve it the ques in in attachment​

Answer 1

${ \underline{ \bold{ \red{ \tt{ Rationalize \: \: \: \: the \: \: \: denominator}}}}}$

${ \huge{ \tt{ \frac{1}{ \sqrt{3} - \sqrt{2} + 1}}} }$

${ \rightarrow{ \green{ \tt{ \: \: \: \frac{1}{ \sqrt{3} - \sqrt{2} + 1 } \times \frac{ \sqrt{3} + \sqrt{2} - 1 }{ \sqrt{3} + \sqrt{2} - 1 } }}}}$

${ \rightarrow{ \tt{ \green{ \frac{ \sqrt{3} + \sqrt{2} + - 1 }{ \sqrt{3}. \sqrt{3} + \sqrt{3}. \sqrt{2} - \sqrt{3}.1 - \sqrt{2} . \sqrt{3} - \sqrt{2} . \sqrt{2} + \sqrt{2} .1 + 1.\sqrt{3} + 1. \sqrt{2} - 1.1}}}}}$

${ \rightarrow{ \tt{ \green{ \frac{ \sqrt{3} + \sqrt{2} - 1 }{3 + \sqrt{6} - \sqrt{3} - \sqrt{6} - 2 + \sqrt{2} + \sqrt{3} + \sqrt{2} - 1}}}} }$

${ \rightarrow{ \tt{ \green{ \frac{ \sqrt{3} + \sqrt{2} - 1 }{ \sqrt{6} - \sqrt{6} + \sqrt{3} - \sqrt{3} + \sqrt{2} + \sqrt{2} + 3 - 2 - 1}}}} }$

${ \rightarrow{ \tt{ \green{ \frac{ \sqrt{3} + \sqrt{2} - 1 }{2 \sqrt{2} } }}}}$

${ \rightarrow{ \tt{ \green{ \frac{ \sqrt{3} + \sqrt{2} - 1 }{2 \sqrt{2} } \times \frac{2 \sqrt{2} }{2 \sqrt{2} } }}}}$

${ \rightarrow{ \tt{ \green {\frac {2 \sqrt{6} + 4 - 2 \sqrt{2} }{8}}}}}$

${ \rightarrow{ \tt{ \green{ \frac{2( \sqrt{6} - \sqrt{2} - 4) }{8}}}}}$

${ \rightarrow{ \huge{ \tt{ \green{ \frac{ \sqrt{6} - \sqrt{2} - 4}{4} }}}}}$