Question

So sánh: A=\(\frac{20^{2015}+1}{20^{2015}-1}\)Và \(B=\frac{20^{2015}-1}{20^{2015}-3}\)

Answer 1

A>1;B<1

A>B

Answer 2

Ta có
\(A=\frac{20^{2015}+1}{20^{2015}-1}=\frac{20^{2015}-1+2}{20^{2015}-1}=1+\frac{2}{20^{2015}-1}\)
\(B=\frac{20^{2015}-1}{20^{2015}-3}=\frac{20^{2015}-3+2}{20^{2015}-3}=1+\frac{2}{20^{2015}-3}\)
Vì \(1+\frac{2}{20^{2015}-1}< 1+\frac{2}{20^{2015}-3}\)
\(\Rightarrow A< B\)

Answer 3

\(A=\frac{20^{2015}+1}{20^{2015}-1}=\frac{20^{2015}-1+2}{20^{2015}-1}=1+\frac{2}{20^{2015}-1}\)

\(\frac{20^{2015}-1}{20^{2015}-3}=\)\(\frac{20^{2015}-3+2}{20^{2015}-3}=1+\frac{2}{20^{2015}-3}\)

vì  \(1+\frac{2}{20^{2015}-1}>1+\frac{2}{20^{2015}-3}\)

vì  tử của hai phân số này bằng nhau nên chúng ta so sánh mẫu, mẫu nào lớn hơn thì mẫu ấy bé hơn nhé

\(\Rightarrow A< B\)