Question

So sánh

a) 10^8+2 / 10^8-1 và 10^8/10^8-3

b) 196/197 +197/198 và 196+197/197+198

c) 20^10 +1/20^10-1 và 20^10 -1 / 20^10 -3

 

Answer 1

\(\frac{10^8+2}{10^8-1}=\frac{10^8-1+3}{10^8-1}=1+\frac{3}{10^8-1}\)

\(\frac{10^8}{10^8-3}=\frac{10^8-3+3}{10^8-3}=1+\frac{3}{10^8-3}\)

Ta có: \(\frac{3}{10^8-1}< \frac{3}{10^8-3}\)

\(\Rightarrow1+\frac{3}{10^8-1}< 1+\frac{3}{10^8-3}\)

\(\Rightarrow\frac{10^8+2}{10^8-1}< \frac{10^8}{10^8-3}\)

Ta có:\(\frac{196}{197}+\frac{197}{198}=\left(1-\frac{1}{197}\right)+\left(1-\frac{1}{198}\right)=2-\frac{1}{197}-\frac{1}{198}>2-1=1\)

Mà \(\frac{196+197}{197+198}< \frac{197+198}{197+198}=1\)

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

c) tương tự câu a

Tham khảo nhé~