B/A= [(10^10 + 1)/(10^11 + 1)]/[(10^11 - 1)/(10^12 - 1)]
= [(10^12 - 1).(10^10 + 1)]/[(10^11 - 1).(10^11 + 1)]
= [(10^22 - 1) + (10^12 - 10^10) ]/((10^22 - 1)
= 1 + (10^12 - 10^10)/(10^22 - 1) > 1
=> B > A
Dấu "/" nghĩa là phân số nhé
Ta có :
\(A=\frac{10^{11}-1}{10^{12}-1}\) \(B=\frac{10^{10}+1}{10^{11}+1}\)
\(10A=\frac{10^{12}-10}{10^{12}-1}\) \(10B=\frac{10^{11}+10}{10^{11}+1}\)
\(10A=\frac{10^{12}-1-9}{10^{12}-1}\) \(10B=\frac{10^{11}+1+9}{10^{11}+1}\)
\(10A=1-\frac{9}{10^{12}-1}\) \(10B=1+\frac{9}{10^{11}+1}\)
Ta thấy \(1-\frac{9}{10^{12}-1}< 1\) mà \(1+\frac{9}{10^{11}+1}>1\)
=> A < B
Vậy A < B
Ủng hộ mk nha !!! ^_^
\(A< \frac{\left(10^{11}-1\right)+11}{\left(10^{12}-1\right)+11}=\frac{10^{11}+10}{10^{12}+10}=\frac{10.\left(10^{10}+1\right)}{10.\left(10^{11}+1\right)}=\frac{10^{10}+1}{10^{11}+1}=B\)= B
ngắn gọn, k cho mik nha