2) \(\left(\dfrac{x+3}{2x+2}-\dfrac{3}{x^2-1}+\dfrac{x+1}{2-2x}\right):\dfrac{9}{5x^2-5}\)
\(=\left(\dfrac{x+3}{2x+2}-\dfrac{3}{x^2-1}-\dfrac{x+1}{2x-2}\right):\dfrac{9}{5x^2-5}\)
\(=\left(\dfrac{x+3}{2\left(x+1\right)}-\dfrac{3}{\left(x-1\right)\left(x+1\right)}-\dfrac{x+1}{2\left(x-1\right)}\right):\dfrac{9}{5x^2-5}\)
\(=\left(\dfrac{\left(x+3\right)\left(x-1\right)}{2\left(x-1\right)\left(x+1\right)}-\dfrac{3.2}{2\left(x-1\right)\left(x+1\right)}-\dfrac{\left(x+1\right)\left(x+1\right)}{2\left(x-1\right)\left(x+1\right)}\right):\dfrac{9}{5x^2-5}\)
\(=\dfrac{\left(x+3\right)\left(x-1\right)-6-\left(x+1\right)^2}{2\left(x-1\right)\left(x+1\right)}:\dfrac{9}{5x^2-5}\)
\(=\dfrac{\left(x^2-x+3x-3\right)-6-\left(x^2+2x+1\right)}{2\left(x-1\right)\left(x+1\right)}:\dfrac{9}{5x^2-5}\)
\(=\dfrac{x^2-x+3x-3-6-x^2-2x-1}{2\left(x-1\right)\left(x+1\right)}:\dfrac{9}{5x^2-5}\)
\(=\dfrac{-10}{2\left(x-1\right)\left(x+1\right)}:\dfrac{9}{5x^2-5}\)
\(=\dfrac{-5}{\left(x-1\right)\left(x+1\right)}.\dfrac{5x^2-5}{9}\)
\(=\dfrac{-5}{\left(x-1\right)\left(x+1\right)}.\dfrac{5\left(x-1\right)\left(x+1\right)}{9}\)
\(=\dfrac{-5.5\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right).9}\)
\(=\dfrac{-25}{9}\)
\(\Rightarrow\) Biểu thức trên không phụ thuộc vào biến x.
\(\Rightarrow dpcm\)
