Co 3 trường hợp:
TH1: a > b
Ta co \(\dfrac{a}{b}-1=\dfrac{a-b}{b}\)
\(\dfrac{a+n}{b+n}-1=\dfrac{a+n-b+n}{b+n}=\dfrac{a-b}{b+n}\)
Vì \(\dfrac{a-b}{b}>\dfrac{a-b}{b+n}\) nên \(\dfrac{a}{b}-1>\dfrac{a+n}{b+n}-1\)
Hay \(\dfrac{a}{b}>\dfrac{a+n}{b+n}\) khi a > b
TH2: a < b
Ta co \(1-\dfrac{a}{b}=\dfrac{b-a}{b}\)
\(1-\dfrac{a+n}{b+n}=\dfrac{b+n-a+n}{b+n}=\dfrac{b-a}{b+n}\)
Vì \(\dfrac{b-a}{b}>\dfrac{b-a}{b+n}\)nên \(1-\dfrac{a}{b}>1-\dfrac{a+n}{b+n}\)
Hay \(\dfrac{a}{b}< \dfrac{a+n}{b+n}\)khi a < b
TH3 : a = b
\(\dfrac{a+n}{b+n}=\dfrac{a}{b}=1\)
Vậy \(\dfrac{a}{b}=\dfrac{a+n}{b+n}\) khi a = b
tick cho mk nha
co gì chưa đung thì xem lại rồi hỏi mk
