\(\frac{x-2}{7}+\frac{x-7}{2}=\frac{7}{x-2}-\frac{2}{x-7}\)ĐKXĐ: \(x\ne2\)và \(x\ne7\)
\(\Leftrightarrow\frac{2\left(x-2\right)}{14}+\frac{7\left(x-7\right)}{14}=\frac{\left(x-7\right)7}{\left(x-7\right)\left(x-2\right)}-\frac{\left(x-2\right)2}{\left(x-7\right)\left(x-2\right)}\)
\(\Leftrightarrow2\left(x-2\right)+7\left(x-7\right)=\left(x-7\right)7-\left(x-2\right)2\)
\(\Leftrightarrow2x-4+7x-49=7x-49-2x-4\)
\(\Leftrightarrow\left(2x-4+7x-49\right)-\left(7x-49-2x-4\right)=0\)
\(\Leftrightarrow2x-4+7x-49+7x+49+2x+4=0\)
\(\Leftrightarrow4x-49x-8-98=0\)
\(\Leftrightarrow x\left(4-49\right)-106=0\)
\(\Leftrightarrow x\left(-45\right)=106\)
\(\Leftrightarrow x=\frac{-106}{45}\)
