Ta có:

\(A=\dfrac{196}{197}+\dfrac{197}{198}\)

\(B=\dfrac{196+197}{197+198}\)

\(=\dfrac{196}{197+198}+\dfrac{197}{197+198}\)

Áp dụng tính chất \(\dfrac{a}{b}>\dfrac{a}{b+m}\) ta có:

\(\left\{{}\begin{matrix}\dfrac{196}{197}>\dfrac{196}{197+198}\\\dfrac{197}{198}>\dfrac{197}{197+198}\end{matrix}\right.\)

\(\Rightarrow\dfrac{196}{197}+\dfrac{197}{198}>\dfrac{196}{197+198}+\dfrac{197}{197+198}=\dfrac{196+197}{197+198}\)

Vậy \(A>B\)

vì \(\dfrac{196}{197+198}< \dfrac{196}{197};\dfrac{197}{197+198}< \dfrac{197}{198}\)

nên \(A=\dfrac{196}{197}+\dfrac{197}{198}>\dfrac{196}{197+198}+\dfrac{197}{197+198}=\dfrac{196+197}{197+198}=B\)

=>A>B

vậy....

A=196/197+197/198>196/197+198 +197/197+198= 196+197/197+198=B

bằng nhau mà

bằng nhau mà ???

 Ta có : \(A=\frac{196}{197}+\frac{197}{198}\)   ;  \(B=\frac{196+197}{197+198}\)\(=\frac{196}{197+198}\) \(+\) \(\frac{197}{197+198}\)

Ta thấy :

\(\frac{196}{197}>\frac{196}{197+198}\)

\(\frac{197}{198}>\frac{197}{197+198}\)

\(\frac{\Rightarrow196}{197}+\frac{197}{198}>\frac{196}{197+198}+\frac{197}{197+198}\)

hay A>B

=>Ta có: B=\(\frac{196}{197+198}\)  + \(\frac{197}{197+198}\)\

Ta có: \(\frac{196}{197+198}\) < \(\frac{196}{197}\) ; \(\frac{197}{197+198}\)< \(\frac{197}{198}\)

=> A= \(\frac{196}{197}\)+ \(\frac{197}{198}\) > \(\frac{196}{197+198}\)  + \(\frac{197}{197+198}\) = B. Vậy A>B

B lớn hơn                                            

Ta có : \(\frac{196}{197}>\frac{196}{198}+\frac{197}{198}=\frac{196+197}{198}>\frac{196+197}{197+198}\)

 \(\Rightarrow A>B\)

A lớn hơn

\(B=\frac{196+197}{197+198}=\frac{196}{197+198}+\frac{197}{197+198}\)

Ta có \(\frac{196}{197}>\frac{196}{197+198}\)và\(\frac{197}{198}>\frac{197}{197+198}\)

=>\(\frac{196}{197}+\frac{197}{198}>\frac{196+197}{197+198}\)

=>A>B

A<B

k nha     Lê Nguyên Khánh