3 radical x - 4 radical y divided by 3 radical x - 2 radical y =
( i think im supposed to use the distributive property, after the conjugate. but didn't know if i could just cancel?
thanks.
To simplify the expression (3√x - 4√y)/(3√x - 2√y), we can indeed use the distributive property after multiplying the numerator and denominator by the conjugate of the denominator.
The conjugate of 3√x - 2√y is 3√x + 2√y.
To multiply the numerator and denominator by the conjugate, we get:
((3√x - 4√y)/(3√x - 2√y)) * ((3√x + 2√y)/(3√x + 2√y))
Using the distributive property, we can then multiply the numerators together and the denominators together:
(3√x * (3√x + 2√y) - 4√y * (3√x + 2√y)) / ((3√x - 2√y) * (3√x + 2√y))
Simplifying the numerators, we have:
(9x + 6√xy - 12√xy - 8y) / ((3√x)^2 - (2√y)^2)
Simplifying the denominator, we have:
(9x + 6√xy - 12√xy - 8y) / (9x - 4y)
Now we can cancel out common terms in the numerator:
(9x + 6√xy - 12√xy - 8y) / (9x - 4y) = (9x - 8y) / (9x - 4y)
Therefore, the simplified expression is (9x - 8y) / (9x - 4y).