Question

Simplify 1 by 2minus root 3 minus 1 by root 3 plus root2 plus 5 by 3 minus root2

Answer 1

Hey there!

$\frac{1}{2 - \sqrt{3} } - \frac{1}{ \sqrt{3} + \sqrt{2} } + \frac{5}{3 - \sqrt{2} }$

Rationalise

$\frac{1}{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } - \frac{1}{ \sqrt{3} + \sqrt{2} } \times \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} - \sqrt{2} } + \frac{5}{3 - \sqrt{2} } \times \frac{3 + \sqrt{2} }{3 + \sqrt{2} }$

$2 + \sqrt{3} - ( \sqrt{3} + \sqrt{2} ) + \frac{5(3 + \sqrt{2}) }{7}$

Opening brackets

$2 + \sqrt{3} - \sqrt{3} + \sqrt{2} + \frac{5(3 + \sqrt{2} }{7}$

$2 + \sqrt{3} - \sqrt{3} + \sqrt{2} + \frac{15 + 5 \sqrt{2} }{7}$

$2 + \sqrt{2} + \frac{15 + 5 \sqrt{2} }{7}$

$\frac{14 + 7 \sqrt{2} + 15 + 5 \sqrt{2} }{7}$

$\frac{29 + 7 \sqrt{2} + 5 \sqrt{2} }{7}$

$\frac{29 + 12 \sqrt{2} }{7}$

Hope it helps!