Ta có :
\(A=\dfrac{10^{10}+1}{10^{10}-1}=\dfrac{10^{10}-1+1+1}{10^{10}-1}=\dfrac{\left(10^{10}-1\right)+1}{10^{10}-1}=1+\dfrac{2}{2016^{10}-1}\) \(\left(1\right)\)
\(B=\dfrac{10^{10}-1}{10^{10}-3}=\dfrac{10^{10}-3-1+3}{10^{10}-3}=\dfrac{\left(10^{10}-3\right)+2}{10^{10}-3}=1+\dfrac{2}{10^{10}-3}\) \(\left(2\right)\)
Từ \(\left(1\right)+\left(2\right)\) \(\Rightarrow\) \(A< B\)
Chúc bn học tốt!!
Ta có A=\(\dfrac{10^{10}+1}{10^{10}-1}=\dfrac{10^{10}-1+2}{10^{10}-1}=\dfrac{10^{10}-1}{10^{10}-1}+\dfrac{2}{10^{10}-1}\)
\(=1+\dfrac{2}{10^{10}-1}\)
B=\(\dfrac{10^{10}-1}{10^{10}-3}=\)\(\dfrac{10^{10}-3+2}{10^{10}-3}\)=\(\dfrac{10^{10}-3}{10^{10}-3}+\dfrac{2}{10^{10}-3}\)
=\(1+\dfrac{2}{10^{10}-3}\)
Vì \(\dfrac{2}{10^{10}-1}>\dfrac{2}{10^{10}-3}\) \(\Rightarrow\) A>B Chúc bạn học tốt tick mik nha
Ta có tính chất: \(\dfrac{a}{b}< 1\Rightarrow\dfrac{a}{b}< \dfrac{a+m}{b+m}\)
Chứng minh:
\(\dfrac{a}{b}=\dfrac{a\cdot\left(b+m\right)}{b\cdot\left(b+m\right)}=\dfrac{ab+am}{b^2+bm}\left(1\right)\)
\(\dfrac{a+m}{b+m}=\dfrac{\left(a+m\right)\cdot b}{\left(b+m\right)\cdot b}=\dfrac{ab+bm}{b^2+bm}\left(2\right)\)
Vì \(\dfrac{a}{b}< 1\Rightarrow a< b\Rightarrow am< bm\Rightarrow ab+am< ab+bm\left(3\right)\)
Từ (1), (2), (3) ta có: \(\dfrac{ab+am}{b^2+bm}< \dfrac{ab+bm}{b^2+bm}\Rightarrow\dfrac{a}{b}< \dfrac{a+m}{b+m}\)
Áp dụng:
Dễ thấy \(B=\dfrac{10^{10}-1}{10^{10}-3}< 1\)
\(\Rightarrow B=\dfrac{10^{10}-1}{10^{10}-3}< \dfrac{10^{10}-1+2}{10^{10}-3+2}=\dfrac{10^{10}+1}{10^{10}-1}=A\\\)
Vậy \(A>B\)
