Question

y = (n^2 + 5n) / (n^2 + 11n + 30)
y = n(n+5) / (n+6)(n+5)
y = n /(n+6)

can someone please explain to me why only -5 is excluded from the domain, when -6 causes division by zero as well.

Answer 1

Good question. I don't know why. Seems incorrect to me

Answer 2

Are you asking how they went from,

\(y=\dfrac{n(n+5)}{(n+6)(n+5)}\)
to
\(y=\dfrac{n}{(n+6)}\)

Answer 3

no, I'm confused about finding the domain for rational functions. I'm getting conflicting information.

Answer 4

some resources ive been looking at would exclude -6 from the domain, and some would not

Answer 5

and i'm not sure why that is.

Answer 6

The domain is everywhere where the equation is valid yes?

Answer 7

yes

Answer 8

By my thinking, -6 should be exluded. But according to my book and wolframalpha, it isn't

Answer 9

So, in that case,
\(n\ne-6\)

Because if it were -6, that would make the denominator zero.

Answer 10

could you look at a pdf for me where it explains the problem i've been having, where it specifically shows what I'm confused about?

Answer 11

Sure.

Answer 12

https://math.temple.edu/~zachhh/rational_expressions.pdf

Answer 13

page 2, simplifyin rational expressions example

Answer 14

continued on page 3, it explains that only -3 is excluded, NOT -2 also, which is exactly the case in this problem I posted here

Answer 15

I understand that the factor which cancels off is a hole, but it should still be excluded from the domain as far as I can tell. But all these resources are telling me that I'm wrong

Answer 16

No, because you have this,

\(\dfrac{(x+2)(x-2)}{(x+2)(x+3)}\rightarrow~\dfrac{\cancel{(x+2)}(x-2)}{\cancel{(x+2)}(x+3)}=\dfrac{(x-2)}{(x+3)}\)

You don't need to worry about it, it simplifies down. At this point, you no longer need to worry about it, it is gone! Is this where you are arriving at problems?

Answer 17

Sorry, I'm too confused to explain myself right. The example I just gave isnt exactly like the one i originally posted. i have a feeling something i'm looking at is wrong and it is just confusing me

Answer 18

in the original example, the only number khan academy accepts as being excluded is -5

Answer 19

is that just a mistake?

Answer 20

by the example in the pdf, -5 should be removable and -6 should be the only excluded number

Answer 21

For the original question at the top? Yeah, if you plug in -5 for (x+6) you would have a 1.... that doesn't really work does it?