Question

So sánh \(A=\frac{10^8+2}{10^8-1}\)\(B=\frac{10^8}{10^8-3}\)

Answer 1

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

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

Vì \(1+\frac{3}{10^8-1}<1+\frac{3}{10^8-3}\) nên A < B

Answer 2

Ta có : 

 A = 10⁸ + 2 / 10 ⁸ - 1 = 1 + 3 / 10 ⁸ - 1

B = 10⁸ / 10 ⁸ - 3 =  1 + 3 / 10⁸ - 3

Vì 3/ 10⁸ - 1 < 3 / 10⁸ - 3=> A < B

Answer 3

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

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

Vì 1 +\(\dfrac{3}{10^8-1}\) < 1 + \(\dfrac{3}{10^8-3}\) nên A < B

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