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\(A=\frac{10^{11}-1}{10^{12}-1}< \frac{10^{11}-1+11}{10^{12}-1+11}\) theo công thức \(\frac{a}{b}< \frac{a+m}{b+m}\)
\(A< \frac{10^{11}+10}{10^{12}+10}=\frac{10^{10}\left(10+1\right)}{10^{11}\left(10+1\right)}=\frac{10^{10}}{10^{11}}\)
\(\Rightarrow\frac{10^{10}}{10^{11}}=\frac{10^{10}\cdot10^{12}}{10^{11}\cdot10^{12}}=\frac{10^{22}}{10^{23}}\)
\(\Leftrightarrow A< \frac{10^{10}}{10^{11}}=\frac{10^{11}}{10^{12}}\)
Lại áp dụng công thức \(\frac{a}{b}< \frac{a+m}{b+m}\)
\(A< \frac{10^{10}}{10^{11}}=\frac{10^{11}}{10^{12}}< \frac{10^{11}+1}{10^{12}+1}=B\)
\(\Leftrightarrow A< B\)
Hoặc \(A< \frac{10^{11}-1+2}{10^{12}-1+2}=\frac{10^{12}+1}{10^{12}+1}\)
..... (EZ)
Ta có :
\(A=\frac{10^{11}-1}{10^{12}-1}< \frac{10^{11}-1+11}{10^{12}-1+11}=\frac{10^{11}+10}{10^{12}+10}=\frac{10\left(10^{10}+1\right)}{10\left(10^{11}+1\right)}=\frac{10^{10}+1}{10^{11}+1}=B\)
\(\Rightarrow A< B\)
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 !!! ^_^
\(10A=\frac{10^{12}-1-9}{10^{12}-1}=\frac{10^{12}-9}{10^{12}}-1\)
\(10B=\frac{10^{11}+1+9}{10^{11}+1}=\frac{10^{11}+9}{10^{11}}+1\)
ta có: \(A=\frac{10^{11}-1}{10^{12}-1}\)
\(\Rightarrow10.A=\frac{10^{12}-10}{10^{12}-1}=\frac{10^{12}-1-9}{10^{12}-1}=\frac{10^{12}-1}{10^{12}-1}-\frac{9}{10^{12}-1}\)\(=1-\frac{9}{10^{12}-1}< 1\)
ta có: \(B=\frac{10^{10}+1}{10^{11}+1}\)
\(\Rightarrow10.B=\frac{10^{11}+10}{10^{11}+1}=\frac{10^{11}+1+9}{10^{11}+1}=\frac{10^{11}+1}{10^{11}+1}+\frac{9}{10^{11}+1}\)\(=1+\frac{9}{10^{11}+1}>1\)
\(\Rightarrow10.A< 10.B\)
\(\Rightarrow A< B\)
\(10A=\frac{10\left(10^{11}-1\right)}{10^{12}-1}=\frac{10^{12}-10}{10^{12}-1}=1-\frac{9}{10^{12}-1}\)
\(10B=\frac{10\left(10^{10}+1\right)}{10^{11}+1}=\frac{10^{11}+10}{10^{11}+1}=1+\frac{9}{10^{11}+1}\)
Vì \(1-\frac{9}{10^{12}-1}< 1+\frac{9}{10^{11}+1}\Rightarrow10A< 10B\)
\(\Rightarrow A< B\)
A>b nha!
để so sánh A và B ta so sánh
\(\frac{10^{11}-1}{10^{12}-1}\)và \(\frac{10^{10}+1}{10^{11}+1}\)
Ta có \(10^{11}-1< 10^{11}+1\)
và \(10^{12}-1>10^{11}+1\)
=> A<B