multiply and simplify
(y^2+10y+25)/(y^2-9)x(y^2+3y)/(y+5)
= (y+5)^2/(y+3)(y-3)) * y(y+3)/(y+5)
= y/(y-3) , y ≠ ±3,-5
Forgot that we had (y+5)^2 upstairs.
y(y+5)/(y+3)
Yup, thanks Steve
(y^2 + 10y + 25)/(y^2 - 9) * (y^2 + 3y)/(y + 5)
(y+5)(y+5)/(y+3)(y-3) * y(y+3)/(y+5)
(y+5)/(y-3) * y/1
y(y+5)/(y-3) or y^2+5y/y-3
To multiply and simplify the given expression:
First, let's factor both numerator and denominator separately.
Numerator:
We have (y^2 + 10y + 25), which is a perfect square trinomial. It can be factored as (y + 5)^2.
Denominator:
For (y^2 - 9), this is a difference of squares, which can be factored as (y - 3)(y + 3).
Next, for (y^2 + 3y), there is no additional factoring we can do in this case.
Lastly, (y + 5) is already factored and cannot be simplified further.
Now, we can rewrite the original expression as:
((y + 5)^2 / ((y - 3)(y + 3))) * (y^2 + 3y) / (y + 5)
Next, cancel out any common factors between the numerator and denominator. In this case, we can observe that (y + 5) appears in both the numerator and denominator, so we can simplify by canceling it out.
Simplifying further, we are left with the following expression:
(y + 5) / ((y - 3)(y + 3))
Therefore, the multiplied and simplified expression is (y + 5) / ((y - 3)(y + 3)).