\(A=\left(\dfrac{2x}{5}+\dfrac{5}{2x-5}\right):\left(\dfrac{4x^2}{125-20x^2}+\dfrac{1}{2x+5}\right)\left(x\ne\pm\dfrac{5}{2}\right).\)
\(A=\dfrac{2x\left(2x-5\right)+5.5}{5\left(2x-5\right)}:\left(\dfrac{4x^2}{5\left(5-2x\right)\left(5+2x\right)}+\dfrac{1}{2x+5}\right).\)
\(A=\dfrac{4x^2-10x+25}{5\left(2x-5\right)}:\left(\dfrac{-4x^2}{5\left(2x-5\right)\left(2x+5\right)}+\dfrac{1}{2x+5}\right).\)
\(A=\dfrac{4x^2-10x+25}{5\left(2x-5\right)}:\dfrac{-4x^2+5\left(2x-5\right)}{5\left(2x-5\right)\left(2x+5\right)}.\)
\(A=\dfrac{4x^2-10x+25}{5\left(2x-5\right)}.\dfrac{5\left(2x-5\right)\left(2x+5\right)}{-4x^2+10x-25}.\)
\(A=-1.\left(2x+5\right).\\ A=-2x-5.\)
Để \(A\le-2.\)
\(\Leftrightarrow-2x-5\le-2.\\ \Leftrightarrow-2x\le3.\\ \Leftrightarrow x\ge\dfrac{-3}{2}.\)
Kết hợp ĐKXĐ.
\(\Rightarrow x\ge\dfrac{-3}{2};x\ne\dfrac{5}{2}.\)
