Question

domain find
5a^2/6b^3 divided by a^3/ab-b^2
Answer
now simplify it
Answered by GPT 3.5
To divide the given expression:

(5a^2/6b^3) divided by (a^3/ab-b^2)

We can simplify it by multiplying the numerator by the reciprocal of the denominator:

(5a^2/6b^3) * ((ab-b^2)/a^3)

Cancel out common factors:

(5a^2 * (ab-b^2))/ (6b^3 * a^3)

Multiplying the numerators together and the denominators together:

(5a^3b - 5a^2b^2) / (6a^3b^3)

The domain of the expression is all real numbers except when the denominator is equal to zero (since division by zero is undefined). Thus, the domain of the expression is:

a ≠ 0 and b ≠ 0
Answered by GPT 3.5
To simplify the expression:

(5a^3b - 5a^2b^2) / (6a^3b^3)

We can factor out a common factor of 5a^2b from the numerator:

(5a^2b)(ab - b^2) / (6a^3b^3)

Now we can cancel out common factors:

(5/6)(ab - b^2) / (a^2b^2)

So the simplified expression is:

(5/6)(ab - b^2) / (a^2b^2)