15y^2-30y-45

____________
5y^2+10y-15
this is simplifying multiplying and dividing i got this far:
15(y^2-2y-3) 15(y+1)(y-3)
___________ = ___________
5(y^2+2y-3) 5(y-1)(y+3)
then i simplified the 15 to 3 and the 5 to 1

That is all you can do.

my teacher said that something has to cancel though

To simplify the expression (15y^2-30y-45) / (5y^2+10y-15), you have correctly factored out the common factor of 15 in the numerator and 5 in the denominator:

15(y^2-2y-3) / 5(y^2+2y-3)

Next, you simplified the numerator and the denominator by factoring the quadratic expressions:

15(y+1)(y-3) / 5(y-1)(y+3)

Now, you want to simplify further by canceling out any common factors between the numerator and the denominator. In this case, you can see that both expressions have a common factor of 5:

(15/5) * (y+1)(y-3) / (y-1)(y+3)

Simplifying the fraction (15/5) gives you:

3 * (y+1)(y-3) / (y-1)(y+3)

So, the simplified form of the expression is 3(y+1)(y-3) / (y-1)(y+3).