First factorise all the components:
x2-9=(x-3)(x+3); x2+4x-12=(x+6)(x-2); x2+2x-3=(x+3)(x-1); x2+5x-6=(x+6)(x-1).
{(x-3)(x+3)/[(x+6)(x-2)]}/{(x+3)(x-1)/[(x+6)(x-1)]}=
{(x-3)(x+3)/[(x+6)(x-2)]}/{(x+3)/(x+6)}.
The division can be replaced by multiplication and inversion of the denominator fraction:
{(x-3)(x+3)/[(x+6)(x-2)]}{(x+6)/(x+3)}=(x-3)(x+3)(x+6)/[(x+6)(x-2)(x+3)]=(x-3)/(x-2).