Question 82876
{{{ (x-7+(12/x))/(x-5+(6/x)) }}} Start with the given expression


{{{ (x/x)((x-7+(12/x))/(x-5+(6/x))) }}} Multiply both top and bottom by x


{{{ (x^2-7x+12)/(x^2-5x+6) }}} Distribute each x


Now factor the top and bottom individually


Factor the numerator

*[invoke quadratic_factoring 1, -7, 12]


Factor the denominator


*[invoke quadratic_factoring 1, -5, 6]



So we after factoring we get:


{{{((x-3)(x-4))/((x-2)(x-3))}}}


{{{(cross((x-3))(x-4))/((x-2)cross((x-3)))}}} Cancel like terms


So everything reduces to:


{{{(x-4)/(x-2)}}}