Final answer:
To divide the given expression (w²-6wx-7x²)(w²+7wx+6x²) by (3w-21x)(w+2x), we factorize the expressions and cancel out the common factors to obtain the simplified expression (w+x)(w+7x)/3.
Step-by-step explanation:
To divide the given expression (w²-6wx-7x²)(w²+7wx+6x²) by (3w-21x)(w+2x), we first factorize the expressions. The numerator can be factored as (w-7x)(w+x)(w+7x)(w+6x), and the denominator can be factored as 3(w-7x)(w+2x). Cancelling out the common factors, we are left with (w+x)(w+7x) divided by 3. Hence, the simplified expression is (w+x)(w+7x)/3.
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