Question

Cho 2 số :

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

So sánh A và B

Answer 1

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

ta có:

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

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

=>A>B

Answer 2

Ta có:

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

Ta xét:

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

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

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

\(\Rightarrow A>B\)