\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+....+\dfrac{1}{38.39}=\dfrac{5}{3}-x\)
=> \(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+......+\dfrac{1}{38}-\dfrac{1}{39}=\dfrac{5}{3}-x\)
=> \(1-\dfrac{1}{39}=\dfrac{5}{3}-x\)
=> \(\dfrac{39}{39}-\dfrac{1}{39}=\dfrac{65}{39}-\dfrac{39x}{39}\)
=> 39-1=65-39x
=> 38=65-39x
=> 39x=-38+65
=> 39x=27
=> x=\(\dfrac{9}{13}\)
vậy x= \(\dfrac{9}{13}\)