$1)a)x^3+x^2-4x-4\\ =x^2(x+1)-4(x+1)\\ =(x^2-4)(x+1)\\ =(x-2)(x+2)(x+1)\\ b)x^4-(4x^2+y^2)+4\\ =x^4-4x^2-y^2+4\\ =x^4-4x^2+4-y^2\\ =(x^2-2)^2-y^2\\ =(x^2-2-y)(x^2-2+y)\\ 2)a)A=\left(\dfrac{x-2}{2x-2}+\dfrac{3}{2x-2}-\dfrac{x+3}{2x+2}\right):\left(1-\dfrac{x-3}{x+1}\right)\\ =2\left(\dfrac{x-2}{x-1}+\dfrac{3}{x-1}-\dfrac{x+3}{x+1}\right):\left(\dfrac{x+1}{x+1}-\dfrac{x-3}{x+1}\right)\\ =2\left(\dfrac{(x-2)(x+1)}{(x-1)(x+1)}+\dfrac{3(x-1)}{(x-1)(x+1)}-\dfrac{(x+3)(x-1)}{(x-1)(x+1)}\right):\dfrac{4}{x+1}\\ =2\left(\dfrac{(x-2)(x+1)+3(x-1)-(x+3)(x-1)}{(x-1)(x+1)}\right).\dfrac{x+1}{4}\\ =\dfrac{x^2-x-2+3x-3-x^2-2x+3}{2(x-1)}\\ =\dfrac{1}{1-x}\\ b)x=2007 \Rightarrow A=-\dfrac{1}{2006}\\ c)A=-1 \Leftrightarrow \dfrac{1}{1-x}=-1\Leftrightarrow x=2\\ 3)a)ĐKXĐ:\left\{\begin{array}{l} 2x-1 \ne0\\ 1-4x^2\ne0\\ 2x+1 \ne0\end{array} \right.\\ \Leftrightarrow x\ne\pm\dfrac{1}{2}\\ b)A=\left(\dfrac{1}{2x-1}+\dfrac{3}{1-4x^2}-\dfrac{2}{2x+1}\right):\left(\dfrac{4x^2+1}{4x^2-1}-1\right)\\ =\left(\dfrac{1}{2x-1}-\dfrac{3}{4x^2-1}-\dfrac{2}{2x+1}\right):\left(\dfrac{4x^2+1}{4x^2-1}-1\right)\\ =\left(\dfrac{2x+1}{(2x-1)(2x+1)}-\dfrac{3}{(2x-1)(2x+1)}-\dfrac{2(2x-1)}{(2x-1)(2x+1)}\right):\left(\dfrac{4x^2+1}{4x^2-1}-\dfrac{4x^2-1}{4x^2-1}\right)\\ =\dfrac{2x+1-3-2(2x-1}{(2x-1)(2x+1)}:\dfrac{1}{4x^2-1}\\ =\dfrac{2x+1-3-4x+2}{(2x-1)(2x+1)}.{(2x-1)(2x+1)}\\ =-2x\\ 4)a)2(x+5)-x^2-5x=0\\ \Leftrightarrow 2(x+5)-x(x+5)=0\\ \Leftrightarrow (2-x)(x+5)=0\\ \Leftrightarrow\left\{\begin{array}{l} x=2\\x=-5\end{array} \right.\\ b)x^2+3x-5=0\\ \Delta=3^2+4.5=29\\ \Rightarrow x=\dfrac{-3\pm\sqrt{29}}{2}$