Question

1 upon 2-root 3 - 1 upon root 3 + root 2 + 5 upon 3- root 2

Answer 1

Step-by-step explanation:

\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