Question

1 divided by √15-√11

Answer 1

$\textbf{ Hello Mate! }$

$\frac{1}{ \sqrt{15} - \sqrt{11} } \\ rationalize \\ \frac{1}{ \sqrt{15} - \sqrt{11} } \times \frac{ \sqrt{15} + \sqrt{11} }{ \sqrt{15} + \sqrt{11} } \\ = \frac{ \sqrt{15} + \sqrt{11} }{ { \sqrt{15} }^{2} - { \sqrt{11} }^{2} } \\ = \frac{ \sqrt{15} - \sqrt{11} }{15 - 11} \\ = \frac{ \sqrt{15} - \sqrt{11} }{4}$

Have great future ahead!

Answer 2

solution

1/(√15-√11)

by rationalizing (√15-√11)

=1/(√15-√11)*(√15+√11)/(√15+√11)

=(√15+√110)/(15-2√165-11)

=(√15+√11)/(4-2√165)

=(√15+√11)/(4-2√165)*(√4+2√165)/(√4+2√165)

= (√15+√11)*(4+2√165)/(16-4*165)

=(4√15+2√2475+4√11+√1815)/16-660

=(4√15+2√2475+4√11+√1815)/-664

=-(4√15+2√2475+4√11+√1815)/664