সরলতম মান নির্ণয় করো :\(\cfrac{2{\sqrt7}}{{\sqrt5}+{\sqrt3}}\)+\(\cfrac{2{\sqrt3}}{{\sqrt7}+{\sqrt5}}\)-\(\cfrac{4{\sqrt5}}{{\sqrt7}+{\sqrt3}}
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\(\cfrac{2{\sqrt7}}{{\sqrt5}+{\sqrt3}}\)+\(\cfrac{2{\sqrt3}}{{\sqrt7}+{\sqrt5}}\)-\(\cfrac{4{\sqrt5}}{{\sqrt7}+{\sqrt3}}\)
\(=\cfrac{2{\sqrt7}({\sqrt5}-{\sqrt3})}{({\sqrt5}+{\sqrt3})({\sqrt5}-{\sqrt3})}\)+\(\cfrac{2{\sqrt3}({\sqrt7}-{\sqrt5})}{({\sqrt7}+{\sqrt5})({\sqrt7}-{\sqrt5})}\)-\(\cfrac{4{\sqrt5}({\sqrt7}-{\sqrt3})}{({\sqrt7}+{\sqrt3})({\sqrt7}-{\sqrt3})}\)
\(=\cfrac{2{\sqrt7}({\sqrt5}-{\sqrt3})}{({\sqrt5})^2-({\sqrt3})^2}\)+\(\cfrac{2{\sqrt3}({\sqrt7}-{\sqrt5})}{({\sqrt7})^2-({\sqrt5})^2}\)-\(\cfrac{4{\sqrt5}({\sqrt7}-{\sqrt3})}{({\sqrt7})^2-({\sqrt3})^2}\)
\(=\cfrac{2{\sqrt7}({\sqrt5}-{\sqrt3})}{5-3}\)+\(\cfrac{2{\sqrt3}({\sqrt7}-{\sqrt5})}{7-5}\)-\(\cfrac{4{\sqrt5}({\sqrt7}-{\sqrt3})}{7-3}\)
\(=\cfrac{\cancel2{\sqrt7}({\sqrt5}-{\sqrt3})}{\cancel2}\)+\(\cfrac{\cancel2{\sqrt3}({\sqrt7}-{\sqrt5})}{\cancel2}\)-\(\cfrac{\cancel4{\sqrt5}({\sqrt7}-{\sqrt3})}{\cancel4}\)
\(=\cancel{\sqrt{35}}-\cancel{\sqrt{21}}+\cancel{\sqrt{21}}-\cancel{\sqrt{15}}-\cancel{\sqrt{35}}+\cancel{\sqrt{15}}\)
\(=0\) [Answer]