Simplify y^2 + y - 20/y^2 - 2y - 8
A)y - 5/y - 2
B)y + 5/y + 2
C)5/2
D)y - 10/y - 4
I chose A. I don't know how to do it.
The only simplification I see is
y^2 -y -20/y^2 -8
Did you omit an = sign?
The y^2 and 1/y^2 terms do not go away, but if it is restated as an equation, it can be manipulated to solve for y.
The rest says: Assume that the denominator is not equal to zero.
Everything else is correct
I see the problem now. You omitted necessary parentheses. There IS no 20/y^2 term
(y^2 + y - 20)/(y^2 - 2y - 8)
Factor numnerator and denominator
[(y+5)/(y-4)]/[(y-4)(y+2)]
= (y+5)/(y+2)
(B)
I cannot say it often enough. When typing equations out on a single line, it is ESSENTIAL that parentheses and brackets be used to avoid ambiguities (confusion) like this.
I see where the confusion was sorry and thank you.
To simplify the expression (y^2 + y - 20)/(y^2 - 2y - 8), we can factor both the numerator and denominator, then cancel out common factors.
Let's start by factoring the numerator and denominator separately:
Numerator (y^2 + y - 20):
We can rewrite this as (y^2 + 5y - 4y - 20) and group it as ((y^2 + 5y) - (4y + 20)). Then, we can factor out common factors from each group, which gives us: y(y + 5) - 4(y + 5). Now, we can see that there is a common factor of (y + 5), so we factor that out and simplify further: (y + 5)(y - 4).
Denominator (y^2 - 2y - 8):
Similarly, we rewrite this as (y^2 - 4y + 2y - 8) and group it as ((y^2 - 4y) + (2y - 8)). Factoring out common factors from each group, we have: y(y - 4) + 2(y - 4). Again, we see a common factor of (y - 4), so we factor that out and simplify further: (y - 4)(y + 2).
Now that we have factored the numerator and denominator, we can cancel out the common factors:
(y + 5)(y - 4)/(y - 4)(y + 2).
As we can see, the (y - 4) terms in both the numerator and denominator can be canceled out, leaving us with:
(y + 5)/(y + 2).
Therefore, the simplified form of (y^2 + y - 20)/(y^2 - 2y - 8) is (y + 5)/(y + 2).
Therefore, option A) y - 5/y - 2 is not the correct answer.