Question 328214
Dividing by a fraction is equivalent to multiplying by its reciprocal,
{{{((x^2-6x+8)/(x^2-7x+12))/((x^2-9x+14)/(x^2-5x+6))=((x^2-6x+8)/(x^2-7x+12))*((x^2-5x+6)/(x^2-9x+14))}}}
Factor each equation.
{{{((x^2-6x+8)/(x^2-7x+12))/((x^2-9x+14)/(x^2-5x+6))=(((x-2)(x-4))/((x-3)(x-4)))*(((x-1)(x-5))/((x-2)(x-7)))}}}
Cancel out common factors.
{{{((x^2-6x+8)/(x^2-7x+12))/((x^2-9x+14)/(x^2-5x+6))=((cross((x-2))cross((x-4)))/((x-3)cross((x-4))))*(((x-1)(x-5))/(cross((x-2))(x-7)))}}}
{{{((x^2-6x+8)/(x^2-7x+12))/((x^2-9x+14)/(x^2-5x+6))=((x-1)(x-5))/((x-3)(x-7))}}}