a2-5a+6=(a-3)(a-2); 2x2+ax-a2=(2x-a)(x+a).
(a2-5a+6)/(2x2+ax-a2)=(a-3)(a-2)/[(2x-a)(x+a)] doesn't simplify any further.
a2+ax+6x2 doesn't simplify through factorisation. (But a2+ax-6x2=(a+3x)(a-2x), so:
(a2+ax-6x2)/(2x2+ax-a2)=(a+3x)(a-2x)/[(2x-a)(x+a)]=-(a+3x)/(x+a).)