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.
(45y-9xy)/(x^2y-25y)
I got an answer of 9y/y(x+5) but it seems to be wrong. Can anyone solve this for me and see what they get? Thank you
(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.
do you see where there is still a mistake?
For example:
5y(x-1)/(25xy²)
=5y(x-1)/(5y(5xy)) ... here, remove 5y, a common factor
=(x-1)/(5xy)
(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?
(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).