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\(\cfrac{8+3√2}{3+√5}-\cfrac{8-3√2}{3-√5}\)
\(=\cfrac{(8+3√2)(3-√5)-(8-3√2)(3+√5)}{(3+√5)(3-√5)} \)
\(=\cfrac{(24-8√5+9√2-3√10)-(24+8√5-9√2-3√10)}{(3)^2-(√5)^2 } \)
\(=\cfrac{24-8√5+9√2-3√10-24-8√5+9√2+3√10}{9-5} \)
\(=\cfrac{-8√5+9√2-8√5+9√2}{9-5} \)
\(=\cfrac{18√2-16√5}{4}\)
\(= \cfrac{2(9√2-8√5)}{4}\)
\(= \cfrac{9√2-8√5}{2}\)