Final answer:
Reciprocals require flipping the numerator and the denominator, leading to option A for the first expression. Multiplying fractions entails multiplying numerators and denominators separately, resulting in option B for the second. The division of polynomials involves factoring and reciprocal operations.
Step-by-step explanation:
When considering the provided expressions, we can address each part one by one. For the reciprocal of the expression -8b / (5b - 6), we must flip the numerator and the denominator. This gives us (5b - 6) / -8b, which corresponds to option A.
In multiplication of fractions, such as 2 / 5a * 6 / 7a^2, we multiply the numerators together and the denominators together separately, resulting in 12 / 35a^3, which corresponds to option B.
In division of polynomial expressions, like (x^2 - 4x - 5) / (x - 2) divided by (2x - 10) / (x^2 - 4), we multiply the first expression by the reciprocal of the second, simplifying if possible. The solution to this is beyond this framework, but the process involves factoring where possible and then multiplying.
Remember the rules of signs in multiplication and division, which state that multiplying or dividing two numbers with the same sign results in a positive number, and with opposite signs results in a negative number.