Question

So sánh 2 biểu thức

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

Answer 1

Ta có: \(A=\dfrac{10^{10}+1}{10^{10}-1}=\dfrac{10^{10}-1+2}{10^{10}-1}=1+\dfrac{2}{10^{10}-1}\)

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

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

\(\Rightarrow A< B\)

Vậy A < B

Answer 2

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

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

Vì \(10^{10}-1>10^{10}-3\) nên ta có

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

Vậy \(A< B\)

Answer 3

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

Vậy A > B

Answer 4

Ko bt có đúng k

Answer 5

nhầm rồi

B = (10^10-1)/(10^10-3) > (10^10-1+2)/(10^10-3+2) = (10^10+1)/(10^10-1)=A

Answer 6

vậy B>A