$i)\dfrac{1}{5x^2+10xy+20y^2}(x^3-8y^3)\\ =\dfrac{1}{5x^2+10xy+20y^2}(x^3-(2y)^3)\\ =\dfrac{1}{5(x^2+2xy+4y^2)}(x-2y)(x^2+2xy+4y^2)\\ =\dfrac{x-2y}{5}\\ j)\dfrac{x^2-ax+bx-ab}{x^2+ax-bx-ab}.\dfrac{x^2+2ax+a^2}{x^2+bx+b^2}\\ =\dfrac{x(x-a)+b(x-a)}{x(x+a)-b(x+a)}.\dfrac{(x+a)^2}{x^2+bx+b^2}\\ =\dfrac{(x+b)(x-a)}{x-b}.\dfrac{(x+a)}{x^2+bx+b^2}\\ =\dfrac{(x+b)(x-a)(x+a)}{(x-b)(x^2+bx+b^2)}\\ =\dfrac{(x+b)(x-a)(x+a)}{(x-b)^3}\\ k)\dfrac{a^2+ax+ba+bx}{a^2-ax-ba+bx}.\dfrac{a^2-ax-bx+ba}{a^2+ax-bx-ba}\\ =\dfrac{a(a+x)+b(a+x)}{a(a-x)-b(a-x)}.\dfrac{a(a-x)+b(a-x)}{a(a+x)-b(a+x)}\\ =\dfrac{(a+b)^2(a+x)(a-x)}{(a-b)^2(a+x)(a-x)}\\ =\dfrac{(a+b)^2}{(a-b)^2}\\ l)\dfrac{x^2+ax-3a-3x}{x^2+3a-ax-3x}.\dfrac{x^2+4x-ax-4a}{x^2+4x+ax+4a}\\ =\dfrac{x(x-3)+a(x-3)}{x(x-3)-a(x-3)}.\dfrac{x(x+4)-a(x+4)}{x(x+4)+a(x+4)}\\ =\dfrac{(x-a)(x+a(x-3)(x+4)}{(x-a)(x+a(x-3)(x+4)}\\ =1$
