Trả lời:
\(x=\frac{9^{11}+2}{9^{11}+3}=\frac{9^{11}+3-1}{9^{11}+3}=\frac{9^{11}+3}{9^{11}+3}-\frac{1}{9^{11}+3}=1-\frac{1}{9^{11}+3}\)
\(y=\frac{9^{12}+2}{9^{12}+3}=\frac{9^{12}+3-1}{9^{12}+3}=\frac{9^{12}+3}{9^{12}+3}-\frac{1}{9^{12}+3}=1-\frac{1}{9^{12}+3}\)
Ta có: \(9^{11}< 9^{12}\)
\(\Leftrightarrow9^{11}+3< 9^{12}+3\)
\(\Leftrightarrow\frac{1}{9^{11}+3}>\frac{1}{9^{12}+3}\)
\(\Leftrightarrow-\frac{1}{9^{11}+3}< -\frac{1}{9^{12}+3}\)
\(\Leftrightarrow1-\frac{1}{9^{11}+3}< 1-\frac{1}{9^{12}+3}\)
\(\Leftrightarrow x< y\)
Vậy x < y
