সরল করি: \(\cfrac{3\sqrt7}{\sqrt5+\sqrt2}-\cfrac{5\sqrt5}{\sqrt2+\sqrt7}+\cfrac{2\sqrt2}{\sqrt7+\sqrt5}\)


\(\cfrac{3√7}{√5+√2}-\cfrac{5√5}{√2+√7}+\cfrac{2√2}{√7+√5}\)
\(=\cfrac{3√7}{√5+√2}-\cfrac{5√5}{√7+√2}+\cfrac{2√2}{√7+√5}\)
\(=\cfrac{3√7(√5-√2)}{(√5+√2)(√5-√2)} -\cfrac{5√5(√7-√2)}{(√7+√2)(√7-√2)} +\cfrac{2√2(√7-√5)}{(√7+√5)(√7-√5)} \)
\(=\cfrac{3√7(√5-√2)}{(√5)^2 -(√2)^2} -\cfrac{5√5(√7-√2)}{(√7)^2 -(√2)^2} +\cfrac{2√2(√7-√5)}{(√7)^2 -(√5)^2} \)
\(=\cfrac{3√7(√5-√2)}{5-2}-\cfrac{5√5(√7-√2)}{7-2}+\cfrac{2√2(√7-√5)}{7-5}\)
\(=\cfrac{3√7(√5-√2)}{3}-\cfrac{5√5(√7-√2)}{5}+\cfrac{2√2(√7-√5)}{2}\)
\(=√7 √5-√2-√5 √7-√2+√2 √7-√5\)
\(=√35-√14-√35+√10+√14-√10\)
\(=0\)

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