সরল করো:
\(\cfrac{\sqrt5}{\sqrt3+\sqrt2}-\cfrac{3\sqrt3}{\sqrt2+\sqrt5}+\cfrac{2\sqrt2}{\sqrt3+\sqrt5}\)
Madhyamik 2011 , 2008
\(\cfrac{\sqrt5}{\sqrt3+\sqrt2}-\cfrac{3\sqrt3}{\sqrt2+\sqrt5}+\cfrac{2\sqrt2}{\sqrt3+\sqrt5}\)
\(=\cfrac{\sqrt5}{\sqrt3+\sqrt2}-\cfrac{3\sqrt3}{\sqrt5+\sqrt2}+\cfrac{2\sqrt2}{\sqrt5+\sqrt3}\)
\(=\cfrac{\sqrt5(\sqrt3-\sqrt2)}{(\sqrt3+\sqrt2)(\sqrt3-\sqrt2)}\)
\(-\cfrac{3\sqrt3(\sqrt5-\sqrt2)}{(\sqrt5+\sqrt2)(\sqrt5-\sqrt2)}\)
\(+\cfrac{2\sqrt2(\sqrt5-\sqrt3)}{(\sqrt5+\sqrt3)(\sqrt5-\sqrt3)}\)
\(=\cfrac{\sqrt5(\sqrt3-\sqrt2)}{3-2}-\cfrac{3\sqrt3(\sqrt5-\sqrt2)}{5-2}\)
\(+\cfrac{2\sqrt2(\sqrt5-\sqrt3)}{5-3}\)
\(=\cfrac{\sqrt5(\sqrt3-\sqrt2)}{3-2}-\cfrac{\cancel3\sqrt3(\sqrt5-\sqrt2)}{\cancel3}\)
\(+\cfrac{\cancel2\sqrt2(\sqrt5-\sqrt3)}{\cancel2}\)
\(=\sqrt{15}-\sqrt{10}-\sqrt{15}+\sqrt6+\sqrt{10}-\sqrt{6}\)
\(=0\)