15x^4y^2-25x^2y^3+45xy/5xy

Question

what is the quotient?

Answer 1

15x⁴y² - 25x²y³ + 45xy / 5xy

The trick here is to factor out things in the numerator that can cancel out in the denominator.

For example, if you look at both parts, you'll see that all of them have a 5 in common, so we can factor that out for cancellation purposes. Similarly, there are 'x's and 'y's in all of the numerator parts, and thus we can factor out one of each of those as well:

5xy(3x³y - 5xy² + 9) / 5xy

 

We now have a 5xy in both the numerator and denominator. Those cancel out to 1, leaving us with the final answer of:

3x³y - 5xy² + 9