`Answer:`
\(A=\frac{196}{197}+\frac{197}{198}\)
\(=\left(1-\frac{1}{197}\right)+\left(1-\frac{1}{198}\right)\)
\(=1-\frac{1}{197}+1-\frac{1}{198}\)
\(=\left(1+1\right)-\left(\frac{1}{197}+\frac{1}{198}\right)\)
\(=2-\left(\frac{1}{197}+\frac{1}{198}\right)\)
Mà \(\frac{1}{197}< \frac{1}{2}\) và \(\frac{1}{198}< \frac{1}{2}\)
\(\Rightarrow\frac{1}{197}+\frac{1}{198}< 1\)
\(\Rightarrow2-\left(\frac{1}{197}+\frac{1}{198}\right)>1\) hay \(A>1\)
Mà \(B=\frac{196+197}{197+198}=\frac{393}{395}< 1\)
`=>A>B`
