\(a,A=\left(\dfrac{x-2}{x+2}-\dfrac{x+2}{x-2}\right).\left(\dfrac{2}{x}-1\right)\)
\(=\left(\dfrac{\left(x-2\right)^2}{\left(x+2\right)\left(x-2\right)}-\dfrac{\left(x+2\right)^2}{\left(x+2\right)\left(x-2\right)}\right).\left(\dfrac{2}{x}-\dfrac{x}{x}\right)\)
\(=\left(\dfrac{x^2-4x+4-x^2-4x-4}{\left(x+2\right)\left(x-2\right)}\right).\left(\dfrac{2-x}{x}\right)\)
\(=\dfrac{-8x}{\left(x+2\right)\left(x-2\right)}.\dfrac{x-2}{-x}\)
\(=\dfrac{8}{x+2}\)
b, Thay \(x=-\dfrac{2}{5}\) vào biểu thức A ,có :
\(\dfrac{8}{-\dfrac{2}{5}+2}=\dfrac{8}{\dfrac{8}{5}}=5\)
Vậy tại x = -2/5 giá trị của A là 5
c, Để \(A=\dfrac{1}{2}\)
\(\Leftrightarrow\dfrac{8}{x+2}=\dfrac{1}{2}\)
\(\Leftrightarrow x+2=16\)
\(\Leftrightarrow x=14\)
Vậy x = 14 thì A = 1/2
