Final Answer:
The simplest form of the given expression is (x-8)².
Step-by-step explanation:
To simplify the given expression, we can start by factoring each term. First, we factor the numerator and denominator separately. The numerator (x²-5x+6) factors to (x-2)(x-3), and the denominator (3x)(9x)/(x-2) (9x-27)/(3) factors to 3x(x-2). Then, we cancel out common factors in the numerator and denominator. After simplifying, we are left with (x-3)/(1)(3x)/(1), which further simplifies to (x-3)(3x), resulting in (x-8)².
This simplification process involves factoring, canceling out common factors, and then multiplying the remaining terms. By following these steps, we arrive at the final answer of (x-8)².
The expression is simplified by factoring and canceling out common factors to reduce it to its simplest form, which is (x-8)². This process ensures that we have simplified the given expression as much as possible, resulting in a clear and concise final answer.