Final answer:
To simplify the expression 8 / (6x + 2w² + 2w) / (6 - w²), it is rewritten as a multiplication by the reciprocal, resulting in 8 × (6 - w²) / (6x + 2w² + 2w), which is in its simplest form given no further information about the variables.
Step-by-step explanation:
The expression given is 8 / (6x + 2w² + 2w) / (6 - w²). To simplify the expression, we note that dividing by a fraction is equivalent to multiplying by its reciprocal. Therefore, we can rewrite the expression as:
8 × (6 - w²) / (6x + 2w² + 2w)
Now, we can look for common factors to simplify. However, without any additional information suggesting that terms can be cancelled or simplified further, there is no obvious simplification available. Thus, the expression is already in its simplest form, assuming that x and w represent variables for which no further information is provided.
In this case, it is helpful to remember to eliminate terms wherever possible to simplify the algebra and check if the answer is reasonable. Since there are no obvious terms to eliminate, we leave it in its simplified multiplied form.