Khi thực hiện phép tính \(\left(\dfrac{x+1}{x+2}+2\right):\left(2-\dfrac{2x^2}{x^2-4}\right)\), ta có kết quả là
\(\dfrac{-3x^2+x+10}{8}\).\(\dfrac{x+1}{x+2}\).\(\dfrac{x^2-4x-10}{8}\).\(\dfrac{3x-5}{x+2}\).Hướng dẫn giải:\(\left(\dfrac{x+1}{x+2}+2\right):\left(2-\dfrac{2x^2}{x^2-4}\right)\)
\(=\left[\dfrac{x+1+2\left(x+2\right)}{x+2}\right]:\left[\dfrac{2\left(x^2-4\right)-2x^2}{x^2-4}\right]\)
\(=\dfrac{3x+5}{x+2}.\dfrac{\left(x-2\right)\left(x+2\right)}{-8}\)
\(=-\dfrac{\left(3x+5\right)\left(x-2\right)}{8}\)
\(=\dfrac{-3x^2+x+10}{8}\).