\(\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{9}+\dfrac{1}{10}\right)\cdot x=\dfrac{1}{9}+\dfrac{2}{8}+\dfrac{3}{7}+...+\dfrac{8}{2}+\dfrac{9}{1}\)
=>\(x\cdot\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{9}+\dfrac{1}{10}\right)=\left(\dfrac{1}{9}+1\right)+\left(\dfrac{2}{8}+1\right)+...+\left(\dfrac{8}{2}+1\right)+1\)
=>\(x\cdot\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{9}+\dfrac{1}{10}\right)=\dfrac{10}{9}+\dfrac{10}{8}+...+\dfrac{10}{2}+\dfrac{10}{10}\)
=>\(x\cdot\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{9}+\dfrac{1}{10}\right)=10\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{9}+\dfrac{1}{10}\right)\)
=>x=10
