Divide
x^3y^2 xy^5
__________ / _________
x^2-3x-18 x^2-x-30
re-typing it ....
x^3y^2/(x^2 - 3x - 18) / ( (xy^5)/(x^2- x- 30) )
looks like it factors nicely , just like the two others I just did for you
Try this one.
To divide the given terms, we need to simplify both the numerator and the denominator, and then divide them.
Let's simplify the numerator first:
x^3y^2 / (x^2 - 3x - 18)
Next, let's simplify the denominator:
xy^5 / (x^2 - x - 30)
Now, let's factor the numerator and denominator to see if we can cancel out any common factors:
In the numerator:
Factor out an x^2: x^3y^2 = x^2 * xy^2
In the denominator:
Factor the quadratic: (x^2 - 3x - 18) = (x - 6)(x + 3)
Notice that we can cancel out an x^2:
(x^2 * xy^2) / (x - 6)(x + 3)
Now, let's simplify the expression further:
The x term in the denominator can be canceled out, which leaves us with:
(xy^2) / (x - 6)(x + 3)
Finally, we have:
(xy^2) / (x - 6)(x + 3)
So, the simplified expression after dividing the given terms is (xy^2) / (x - 6)(x + 3).