Lấy \(x_1;x_2\in\left(1;+\infty\right)\left(x_1\ne x_2\right)\)
\(\Rightarrow y_1-y_2=\frac{4x_1}{x_1-1}-\frac{4x_2}{x_2-1}=\frac{4x_1\left(x_2-1\right)-4x_2\left(x_1-1\right)}{\left(x_1-1\right)\left(x_2-1\right)}=-\frac{4\left(x_1-x_2\right)}{\left(x_1-1\right)\left(x_2-1\right)}\)
\(\Rightarrow I=\frac{y_1-y_2}{x_1-x_2}=-\frac{4}{\left(x_1-1\right)\left(x_2-1\right)}\)
Do \(x_1;x_2\in\left(1;+\infty\right)\Rightarrow x_1-1>0;x_2-1>0\Rightarrow\left(x_1-1\right)\left(x_2-1\right)>0\)
\(\Rightarrow I=-\frac{4}{\left(x_1-1\right)\left(x_2-1\right)}< 0\)
\(\Rightarrow\) Hàm số nghịch biến trên \(\left(1;+\infty\right)\)
