Final answer:
The result of the expression 5a^2/6b^3 divided by a^3/ab-b^2 is (5/6)(ab-b^2)/(a^2b^3), which corresponds to option b) (5a/6b).
Step-by-step explanation:
To divide two fractions, we need to multiply the first fraction by the reciprocal of the second fraction.
In this case, the expression 5a^2/6b^3 divided by a^3/ab-b^2 becomes:
(5a^2/6b^3) * (ab-b^2/a^3)
Simplifying this further, we can cancel out common factors:
=(5/6)(a/a^3)(ab-b^2)/(b^3)
=(5/6)(1/a^2)(ab-b^2)/(b^3)
=(5/6)(ab-b^2)/(a^2b^3)
So, the result of the expression is (5/6)(ab-b^2)/(a^2b^3), which corresponds to option b) (5a/6b).
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