What is the result of the expression 5a^2/6b^3 divided by a^3/ab-b^2? a) (5/6b) b) (5a/6b) c) (5a^2/6b^3) d) (5/6)

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asked Dec 26, 2024 202k views

1 Answer

Shun Yamada · Answer 1 · 2024-12-31T09:35:44+0000

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).

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).