Final answer:
To fully simplify the given expression, we need to factor the numerator and denominator and then combine the like terms. The final simplified form is ((x-3)(x-4)(x-7)(x+7)(3x-7)(x-1))/(x-3)²(x-4)(x-4).
Step-by-step explanation:
To fully simplify this expression, we need to combine like terms and perform any necessary operations.
First, let's simplify (x²-7x+12)/(x²-8x+15)². We can simplify the numerator by factoring it as (x-3)(x-4), and the denominator can be factored as (x-3)².
Next, we simplify (x²-49)(3x²-36x+105)/(x-4). The numerator can be factored as (x-7)(x+7) and (3x-7)(x-1), and the denominator is just (x-4).
Lastly, we multiply the simplified numerators and divide by the simplified denominator. Combining all the factors, we get ((x-3)(x-4)(x-7)(x+7)(3x-7)(x-1))/(x-3)²(x-4)(x-4).
This is the fully simplified form of the expression.