1/1.2+2/2.3
=1/1.2+1/2.3+1/2.3
=1/1-1/2+1/2-1/3+1/6
=1/1-1/2+1/6
=1/2+1/6
=2/3
\(\dfrac{1}{1.2}+\dfrac{2}{2.3}=\dfrac{1}{2}+\dfrac{1}{3}=\dfrac{3}{6}+\dfrac{2}{6}=\dfrac{5}{6}\)
\(\dfrac{1}{1\cdot2}+\dfrac{2}{2\cdot3}=\left(1-\dfrac{1}{2}\right)+2\left(\dfrac{1}{2}-\dfrac{1}{3}\right)=\left(\dfrac{2}{2}-\dfrac{1}{2}\right)+2\left(\dfrac{3}{6}-\dfrac{2}{6}\right)=\dfrac{1}{2}+2\left(\dfrac{1}{6}\right)=\dfrac{1}{2}+\dfrac{1}{3}=\dfrac{3}{6}+\dfrac{2}{6}=\dfrac{5}{6}\)