domain find
5a^2/6b^3 divided by a^3/ab-b^2
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
now simplify it
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)
To simplify the expression (5a^2/6b^3) ÷ (a^3/ab-b^2), you can follow these steps:
Step 1: Rewrite the expression using division as multiplication by the reciprocal.
(5a^2/6b^3) ÷ (a^3/ab-b^2) = (5a^2/6b^3) × (ab-b^2/a^3)
Step 2: Simplify the numerator of the fraction.
The numerator can be simplified as follows:
5a^2 × (ab - b^2) = 5a^3b - 5a^2b^2
Step 3: Simplify the denominator of the fraction.
The denominator can be simplified as follows:
6b^3 × a^3 = 6a^3b^3
Step 4: Combine the simplified numerator and denominator to get the final result.
(5a^3b - 5a^2b^2) / (6a^3b^3)