ĐK: \(x\ne\pm4\)
\(Q=\left(\dfrac{1}{\left(x+4\right)^2}-\dfrac{1}{\left(x-4\right)^2}\right):\left(\dfrac{x-4}{x^2-16}+\dfrac{x+4}{x^2-16}\right)\)
\(=\left(\dfrac{x^2-8x+16}{\left(x+4\right)^2\left(x-4\right)^2}-\dfrac{x^2+8x+16}{\left(x-4\right)^2\left(x+4\right)^2}\right):\left(\dfrac{x-4+x+4}{x^2-16}\right)\\ =\left(\dfrac{x^2-8x+16-x^2-8x-16}{\left(x+4\right)^2\left(x-4\right)^2}\right):\dfrac{2x}{x^2-16}\\ =\dfrac{-16x\left(x+4\right)\left(x-4\right)}{2x\left(x+4\right)^2\left(x-4\right)^2}\\ =\dfrac{-8}{\left(x+4\right)\left(x-4\right)}=\dfrac{-8}{x^2-16}\)
\(=\dfrac{x^2-8x+16-x^2-8x-16}{\left(x-4\right)^2\left(x+4\right)^2}:\dfrac{x-4+x+4}{\left(x+4\right)\left(x-4\right)}\)
\(=\dfrac{-16x}{\left(x-4\right)^2\left(x+4\right)^2}\cdot\dfrac{\left(x+4\right)\left(x-4\right)}{2x}=-\dfrac{8}{\left(x-4\right)\left(x+4\right)}\)
