সরল করি: \(\cfrac{3√2}{√3+√6}-\cfrac{4√3}{√6+√2}+\cfrac{√6}{√2+√3}\)
\(\cfrac{3√2}{√3+√6}-\cfrac{4√3}{√6+√2}+\cfrac{√6}{√2+√3}\)
\(=\cfrac{3√2}{√6+√3}-\cfrac{4√3}{√6+√2}+\cfrac{√6}{√3+√2}\)
\(=\cfrac{3√2 (√6-√3)}{(√6+√3)(√6-√3)} -\cfrac{4√3 (√6-√2)}{(√6+√2)(√6-√2)} +\cfrac{√6 (√3-√2)}{(√3+√2)(√3-√2)}\)
\(=\cfrac{3√2 (√6-√3)}{6-3}-\cfrac{4√3 (√6-√2)}{6-2}+\cfrac{√6 (√3-√2)}{3-2}\)
\(=\cfrac{3√2 (√6-√3)}{3}-\cfrac{4√3 (√6-√2)}{4}+\cfrac{√6 (√3-√2)}{1}\)
\(=√2 (√6-√3)-√3 (√6-√2)+√6 (√3-√2)\)
\(=√12-√6-√18+√6+√18-√12\)
\(=0\)
Similar Questions