Question

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

Hỏi trong hai số A và B , số nào lớn hơn

Answer 1

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 \(A>B\)