What is the simplified form of y^2 - y - 12 / y^2 + 8y + 15
I will assume you mean
(y^2 - y - 12) / )y^2 + 8y + 15)
= (y-4)(y+3)/( (y+5)(y+3) )
= (y-4)/(y+5) , y ≠ -3
To simplify the expression (y^2 - y - 12)/(y^2 + 8y + 15), we need to factor the numerator and denominator.
The numerator (y^2 - y - 12) can be factored as (y - 4)(y + 3).
The denominator (y^2 + 8y + 15) can be factored as (y + 3)(y + 5).
So, the expression can be written as [(y - 4)(y + 3)] / [(y + 3)(y + 5)].
Now, we can cancel out the common factor (y + 3) in both the numerator and denominator.
The simplified form of the expression is (y - 4) / (y + 5).
To find the simplified form of the expression (y^2 - y - 12) / (y^2 + 8y + 15), we can factor the numerator and denominator and then simplify the expression.
Step 1: Factor the numerator and denominator:
The numerator (y^2 - y - 12) can be factored as (y - 4)(y + 3).
The denominator (y^2 + 8y + 15) can be factored as (y + 3)(y + 5).
Step 2: Simplify the expression:
Now, we can cancel out the common factors from the numerator and denominator. In this case, we have a common factor of (y + 3).
So, the simplified form of the expression is:
(y - 4) / (y + 5)
Therefore, the simplified form of (y^2 - y - 12) / (y^2 + 8y + 15) is (y - 4) / (y + 5).