Simplify the rational expression.

First take out obvious common factors

(45y-9xy)/(x^2y-25y)
=9y(5-9x)/y(x²-25)

cancel out the common factor y from the numerator and denominator and see if there are other factoring you can do.

I did that u get 9y(5-9x)/((x-5)(x+5)) but it is still wrong

Did you leave the "y" in the numerator?

sorry what I was suppose to write was 9y(5-9x)/y((x-5)(x+5))

do you see where there is still a mistake?

If you have a "y" both in the numerator and denominator, you can cancel them out as long as y≠0.

For example:
5y(x-1)/(25xy²)
=5y(x-1)/(5y(5xy)) ... here, remove 5y, a common factor
=(x-1)/(5xy)

so will the final answer be 9(5-9x)/((x-5)(x+5)) ?

Correct!

It still shows me as wrong when I submit online

Sorry, there was a mistake in:

(45y-9xy)/(x^2y-25y)
=9y(5-9x)/y(x²-25)

Should have read:
(45y-9xy)/(x^2y-25y)
=9y(5-x)/y(x²-25)

Now can you figure out the answer and try again?

To simplify the rational expression (45y-9xy)/(x^2y-25y), we can first factor out the common term '9y' from the numerator:

(45y-9xy)/(x^2y-25y) = 9y(5-x)/(y(x^2-25))

Next, the denominator can be factored as the difference of squares:

x^2-25 = (x+5)(x-5)

Applying this factorization to the expression:

9y(5-x)/(y(x^2-25)) = 9y(5-x)/(y(x+5)(x-5))

Now, we can cancel out the common factors:

9y cancels y:
= (5-x)/(x+5)(x-5)

Therefore, the simplified rational expression is (5-x)/(x+5)(x-5).