Ta có:

\(A=\frac{20^{10}+1}{20^{10}-1}=1\)

\(B=\frac{20^{10}-1}{20^{10}-3}=1\)

Vậy A và B bằng nhau

Tính A và B rồi ta so sánh:

A = \(\frac{20^{10}+1}{20^{10}-1}\) = \(1\)

B = \(\frac{20^{10}-1}{20^{10}-3}\) = \(1\)

Mà \(1\) = \(1\)

Nên: A = B

A=(20^10+1/20^10-1)=(20^10-1+2/20^10-1)=(20^10-1/20^10-1)+(2/20^10-1)=1+(2/20^10-1).

Tương tự ,B=1+(2/20^10-3).
Vì 2/20^10-1>2/20^10-3(vì 20^10-1>20^10-3).

=>A<B.

Vậy A<B.

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ta thấy B>1 nên B=\(\frac{20^{10}-1}{20^{10}-3}\)>\(\frac{20^{10}-1+2}{20^{100}-3+2}\)=\(\frac{20^{10}+1}{20^{10}-1}\)=A

vậy B>A

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Vì \(20^{10}-1>20^{10}-3\)

\(\Rightarrow B=\frac{20^{10}-1}{20^{10}-3}>\frac{20^{10}-1+2}{20^{10}-3+2}=\frac{20^{10}+1}{20^{10}-1}=A\)

vậy \(A< B\)

\(A=\frac{20^{10}+1}{20^{10}-1}=\frac{20^{10}-1}{20^{10}-1}+\frac{2}{20^{10}-1}=1+\frac{2}{20^{10}-1}\)

\(B=\frac{20^{10}-1}{20^{10}-3}=\frac{20^{10}-3}{20^{10}-3}+\frac{2}{20^{10}-3}=1+\frac{2}{20^{10}-3}\)

\(20^{10}-1>20^{10}-3\Rightarrow\frac{2}{20^{10}-1}< \frac{2}{20^{10}-3}\)

=> A < B

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

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

Vì \(\frac{2}{2^{10}-1}