Question

Simplify:1 by 2-root3 - 1 by root3+root2 + 5 by 3-root2

Answer 1

$\frac{1}{2 - \sqrt{3} } - \frac{1}{ \sqrt{3} + \sqrt{2} } + \frac{5}{3 - \sqrt{2} }$
now we factorise each expression one by one
$\frac{1}{2 - \sqrt{3} } = 2 + \sqrt{3}$
$\frac{5}{3 - \sqrt{2} } = \frac{5(3 + \sqrt{2}) }{9 - 2} = \frac{15 + 5 \sqrt{2} }{7}$

$\frac{1}{ \sqrt{3} + \sqrt{2} } = \sqrt{3} - \sqrt{2}$
now simplification
2 + \sqrt{3} [/tex]-(\sqrt{3} - \sqrt{2} [/tex])+\frac{15 + 5 \sqrt{2} }{7} [/tex]
=\frac{15 + 5 \sqrt{2}+14+7\sqrt{2} }{7} [/tex]=\frac{29 + 12 \sqrt{2} }{7} [/tex]
hope it helped you