\(\dfrac{1}{2}\cdot x\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{22}\right)=\dfrac{1}{21}+\dfrac{2}{20}+\dfrac{3}{19}+...+\dfrac{20}{2}+\dfrac{21}{1}\)
=>\(\dfrac{1}{2}\cdot x\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{22}\right)=\left(\dfrac{1}{21}+1\right)+\left(\dfrac{2}{20}+1\right)+\left(\dfrac{3}{19}+1\right)+...+\left(\dfrac{20}{2}+1\right)+1\)
=>\(\dfrac{1}{2}\cdot x\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{22}\right)=\dfrac{22}{21}+\dfrac{22}{20}+...+\dfrac{22}{2}+\dfrac{22}{22}\)
=>\(\dfrac{1}{2}\cdot x\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{22}\right)=22\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{22}\right)\)
=>\(\dfrac{1}{2}\cdot x=22\)
=>x=44
