Simplify a2 - 5a + 6 / 2x2 + ax – a2

Question

Simplify a² + ax + 6x² / 2x² + ax – a²

Answer 1

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).)