Question

[phạm thị thu phương]

1, So sánh

C=\(\dfrac{10^{11}-1}{10^{12}-1}\) và D=\(\dfrac{10^{10}+1}{10^{11}+1}\)

Answer 1

[Nguyễn Huy Tú]

Ta có: \(10C=\dfrac{10^{12}-10}{10^{12}-1}=1-\dfrac{9}{10^{12}-1}\)

\(10D=\dfrac{10^{11}+10}{10^{11}+1}=1+\dfrac{9}{10^{11}+1}\)

\(\dfrac{9}{10^{12}-1}< \dfrac{9}{10^{12}+1}\Rightarrow1-\dfrac{9}{10^{12}-1}< 1+\dfrac{9}{10^{11}+1}\Rightarrow10A< 10B\)

\(\Rightarrow A< B\)

Vậy A < B

Answer 2

[Nguyen Thi Huong Ly]

10C=\(\dfrac{10.\left(10^{11}-1\right)}{10^{12}-1}\)=\(\dfrac{10^{12}-10}{10^{12}-1}\)=\(\dfrac{10^{12}-1-9}{1012-1}\)=1-\(\dfrac{9}{10^{12}-1}\)<1 (1)

10D=\(\dfrac{10.\left(10^{10}+1\right)}{10^{11}+1}\)=\(\dfrac{10^{11}+10}{10^{11}+1}\)=\(\dfrac{10^{11}+1+9}{10^{11}+1}\)=1+\(\dfrac{9}{10^{11}+1}\)>1 (2)

(1),(2)=> 1-\(\dfrac{9}{10^{12}-1}\)<1+\(\dfrac{9}{10^{11}+1}\)

hay 10C<10D

=>C<D