\(A=\dfrac{10^{12}+6}{10^{12}-11}\)

\(\Rightarrow A=\dfrac{10^{12}-11+17}{10^{12}-11}\)

\(\Rightarrow A=\dfrac{10^{12}-11}{10^{12}-11}+\dfrac{17}{10^{12}-11}\)

\(\Rightarrow A=1-\dfrac{17}{10^{12}-11}\)

\(B=\dfrac{10^{11}+5}{10^{11}-12}\)

\(\Rightarrow B=\dfrac{10^{11}-12+17}{10^{11}-12}\)

\(\Rightarrow B=\dfrac{10^{11}-12}{10^{11}-12}+\dfrac{17}{10^{11}-12}\)

\(\Rightarrow B=1-\dfrac{17}{10^{11}-12}\)

Vậy ta cần so sánh \(1-\dfrac{17}{10^{12}-11}\) và \(1-\dfrac{17}{10^{11}-12}\) 

Ta thấy \(\left(10^{12}-11\right)>\left(10^{11}-12\right)\) và 2 phân số trên cùng tử số 17 nên \(\dfrac{17}{10^{12}-11}< \dfrac{17}{10^{11}-12}\)

Vậy \(1-\dfrac{17}{10^{12}-11}>1-\dfrac{17}{10^{11}-12}\) hay \(A>B\)

Cảm ơn bạn nhé!

a. 19/10 > 10/11

b. 11/10 = 12/11

c. 9/10 = 10/11

a)\(\dfrac{19}{10}>\dfrac{10}{11}\)

b)\(\dfrac{11}{10}=\dfrac{12}{11}\)

c)\(\dfrac{9}{10}< \dfrac{10}{11}\)

- 3/4 < 4/3 (vì 3/4 < 1 < 4/3 nên 3/4 < 4/3).

- 10/7 > 7/9 (vì 10/7 > 1 > 7/9 nên 10/7 > 7/9).

- 12/11 > 11/10 (vì 12/11 > 1 > 11/10 nên 12/11 > 11/10).

3/4 < 4/3 vi 3/4 be hon 1con 4/3 lon hon 1

10/7 > 7/9 vi 10/7 lon hon 1 con 7/9 be hon 1

12/11 > 11/10 vi 12/11 lon hon 1 con 11/10 be hon 1

Ta thấy:  

\(\frac{9}{10}< 1< \frac{12}{11}\)

\(\Rightarrow\frac{9}{10}< \frac{12}{11}\)

a / 12 / 11

b/   16/17

ĐỀ : \(A=\frac{10^{11}-1}{10^{12}-1}\)và \(B=\frac{10^{10}+1}{10^{11}+1}\).

Ta có : \(10A=\frac{10\left(10^{11}-1\right)}{10^{12}-1}=\frac{10^{12}-10}{10^{12}-1}=\frac{10^{12}-1-9}{10^{12}-1}\)\(=1-\frac{9}{10^{12}-1}\).

            \(10B=\frac{10\left(10^{10}+1\right)}{10^{11}+1}=\frac{10^{11}+10}{10^{11}+1}=\frac{10^{11}+1+9}{10^{11}+1}\)\(=1+\frac{9}{10^{11}+1}\).

Ta so sánh : \(1-\frac{9}{10^{12}-1}< 1+\frac{9}{10^{11}+1}\)hay \(10A< 10B.\)

\(\Rightarrow A< B\left(đpcm\right)\)

\(\dfrac{11}{10}=\dfrac{11\cdot11}{10\cdot11}=\dfrac{121}{110}\)

\(\dfrac{10}{11}=\dfrac{10\cdot10}{11\cdot10}=\dfrac{100}{110}\)

có `121/110 > 100/110` nên `11/10 > 10/11`

\(\dfrac{11}{10}>1>\dfrac{10}{11}\)

Chúc em học tốt!

nhanh nhanh lên nào

quy đồng đi bạn

Nhớ là 2 cách nha

a: 11/10>1>10/11

b: 4/9=44/99

c: 15/25=3/5

12/15=4/5

mà 3/5<4/5

nên 15/25<12/15

a: 11/10>1>10/11

b: 4/9=44/99

c: 15/25=3/5

12/15=4/5

mà 3/5<4/5

nên 15/25<12/15

Ta có : 

\(\frac{10}{11}>\frac{10}{11+12};\frac{11}{12}>\frac{11}{11+12}\)

\(\Rightarrow\frac{10}{11}+\frac{11}{12}>\frac{10}{11+12}+\frac{11}{11+12}\)

\(\Rightarrow\frac{10}{11}+\frac{11}{12}>\frac{10+11}{11+12}\)

Vậy \(\frac{10}{11}+\frac{11}{12}>\frac{10+11}{11+12}\)

Chúc bạn học tốt !!! 

ta có: \(\frac{10+11}{11+12}=\frac{10}{11+12}+\frac{11}{11+12}\)

mà \(\frac{10}{11}>\frac{10}{11+12}\)

\(\frac{11}{12}>\frac{11}{11+12}\)

\(\Rightarrow\frac{10}{11}+\frac{11}{12}>\frac{10}{11+12}+\frac{11}{11+12}\)

\(\Rightarrow\frac{10}{11}+\frac{11}{12}>\frac{10+11}{11+12}\)

 Ta có :  10 + 11 / 11 + 12 = (10/11 + 12)     +      (11/ 11+ 12 )

        Vì 10/11 > 10/ 11 +12

             11/12 > 11/ 11 + 12

 =>    10/11+11/12 > 10+11/11+12