Question

So sánh:

A=\(\dfrac{10^8+2}{10^8-1}\)

B=\(\dfrac{10^8}{10^8-3}\)

Answer 1

A>B

Answer 2

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

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

Vì \(\dfrac{3}{10^8-1}< \dfrac{3}{10^8-3}\)

Nên \(1+\dfrac{3}{10^8-1}< 1+\dfrac{3}{10^8-3}\)

Vậy A < B.