\(\sqrt7(\sqrt5–\sqrt2)−\sqrt5(\sqrt7–\sqrt2)\) \(+\cfrac{2\sqrt2}{\sqrt5+\sqrt7}\)
\(=\sqrt7(\sqrt5–\sqrt2)−\sqrt5(\sqrt7–\sqrt2)+\cfrac{2√2}{√7+√5}\)
\(=\sqrt7(\sqrt5–\sqrt2)−\sqrt5(\sqrt7–\sqrt2)\)
\( +\cfrac{2√2 (√7-√5)}{(√7+√5)(√7-√5)}\)
\(=\sqrt7(\sqrt5–\sqrt2)−\sqrt5(\sqrt7–\sqrt2)\)
\(+\cfrac{2√2 (√7-√5)}{7-5}\)
\(=\sqrt7(\sqrt5–\sqrt2)−\sqrt5(\sqrt7–\sqrt2)\)
\(+\cfrac{\cancel2√2 (√7-√5)}{\cancel2}\)
\(=√35-√14-√35+√10+√14-√10\)
\(=0\)