Simplify : (i) (3√2 - 2√3)/(3√2 + 2√3) - (√12)/(√3 - √2) (ii) (√5 + √3)/(√5 - √3) + (√5-√3)/(√5 + √3)

Question

Simplify:

(i) \(\frac{3\sqrt2-2\sqrt3}{3\sqrt2+2\sqrt3}-\frac{\sqrt12}{\sqrt3-\sqrt2}\)

(ii) \(\frac{\sqrt5+\sqrt3}{\sqrt5-\sqrt3}+\frac{\sqrt5-\sqrt3}{\sqrt5+\sqrt3}\)

Answer 1

(i) \(\frac{3\sqrt2-2\sqrt3}{3\sqrt2+2\sqrt3}+\frac{\sqrt12}{\sqrt3-\sqrt2}\) 

= \(\frac{(3\sqrt2-2\sqrt3)(3\sqrt2-2\sqrt3)}{18-12}\) + \(\frac{2\sqrt3(\sqrt3+\sqrt2)}{3-2}\)

(ii) \(\frac{\sqrt5+\sqrt3}{\sqrt5-\sqrt3}+\frac{\sqrt5-\sqrt3}{\sqrt5+\sqrt3}\) 

= \(\frac{[(\sqrt5+\sqrt3)(\sqrt5+\sqrt3)+(\sqrt5-\sqrt3)(\sqrt5-\sqrt3)]}{5-3}\) 

= \(\frac{8+2\sqrt15+8-2\sqrt15}{2}\) 

= 8