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

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

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

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

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

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

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

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

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) (-12).8 < (-19).3.

b) 11.(-2) > (-3).10.

c) (-16). 10 > (-32).11.

d) (-17).3 < (-22).2.

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 \(\frac{10}{11}>\frac{10}{11+12}\)

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

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

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

a) Ta có

A = n / n+1 = 1-(1/n+1)

A = n+2 / n+3 = 1-(1/n+3)

Vì 1/n+1 > 1/n+3

=> n/n+1 < n+2/n+3 

=> A<B

a)10/13>11/12

b)11/49<13/47

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