Question

so sánh

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

Answer 1

Ta có :\(A=\frac{10^{10}+1}{10^{10}-1}\)

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

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

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

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

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

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

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

Vì \(\frac{2}{10^{10}-1}< \frac{2}{10^{10}-3}\)

\(\Rightarrow1+\frac{2}{10^{10}-1}< 1+\frac{2}{10^{10}-3}\)

\(\Rightarrow A< B\)

Vậy A<B