For what value(s) of r is r^2+5r+6/r+2 equal to 0?

A) -2 only
B) -3 only
C) 3 only
D)-2 or -3
E) 2 or 3

I got A but it is incorrect and I'm still confused

Thanks

I think the problem is supposed to be this:

f(r)=r^2+5r+6/(r+2)

obviously, r cannot be -2.
Try -3. This problem is not rocket science. Plug in the values and compute

if r = -2, then the denominator is zero...a big no-no

factor the numerator and go with B

maybe Scott is right, you meant

(r^2+5r+6)/(r+2 )

it is difficult to solve these if the function is not written with precision

So the zero can only come from the numerator, thus

r^2 + 5r + 6 = 0
(r+2)(r+3) = 0
r = -2 or r = -3

BUT, as noted in your other replies, r cannot be -2

so r = -3
which is C

To find the values of r for which the expression (r^2 + 5r + 6) / (r + 2) equals zero, you need to solve the equation by setting the expression equal to zero.

(r^2 + 5r + 6) / (r + 2) = 0

Firstly, observe that the numerator can be factored as:

(r + 2)(r + 3)

So the equation becomes:

(r + 2)(r + 3) / (r + 2) = 0

Now cancel out the common factor of (r + 2) on both sides:

(r + 3) = 0

To find the value of r, solve the equation:

r + 3 = 0
r = -3

Therefore, the value of r that makes the expression equal to zero is -3.

So, the correct answer is B) -3 only.

It seems you selected A) -2, which is incorrect because -2 cancels out in the numerator, but since the denominator is (r + 2), it cannot be zero in this case.