Question

I am currently stuck solving this limit the answer is 1 but I get 1/3. I don't know what I am doing wrong, can someone help solve limx-(-2) x^4+5x^3+6x^2/x^2(x+1)-4(x+1)

Answer 1

With steps and an explanation as to why?

Answer 2

limit as x approaches -2 of (x^4+ 5x^3 + 6x^2) / ((x^2)(x+1)-4(x+1)) ?

Answer 3

is that the question?

Answer 4

Yes that is the question

Answer 5

could you tell us how you factored the numerator in the denominator ?

Answer 6

well first I factored the numerator and got (x^2 (x^2+5x+6))/x^2(x+1)-4(x+1) and crossed out the x^2 to get (x^2+5x+6)/-3(x+1)

Answer 7

that is your problem then you can only cancel out what common factors the denominator and numerator have
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basically you aren't done factoring either one

Answer 8

I think @billj5 wants to assist you
so I will let him continue if he wants.

Answer 9

Okay. If I factored further I would get (x+2)(x+3)/-3(x+1). Correct?

Answer 10

if he is still there

Answer 11

well no you can't cancel the x^2 's because you don't have a factor x^2 on bottom

Answer 12

oh, so that's where I went wrong.

Answer 13

\[x^2(x+1)-4(x+1) \\ (x+1)(x^2-4)\]

Answer 14

Oh, okay. I understand, I'm going to go fix my mistake. Thank you

Answer 15

You can't cancel out the x^2 because it isn't a factor. Correct?

Answer 16

right if you had had:
\[\frac{x^2(x^2+5x+6)}{x^2(x-1)}\]
you could have canceled the x^2 on top and bottom

Answer 17

but we had
\[\frac{x^2(x^2+5x+6)}{(x+1)(x^2-4)}\]
and there is no x^2 factor on bottom

Answer 18

Thank you so much. :)

Answer 19

you can do a little more factoring on top and bottom
and you should see a common factor

Answer 20

Okay, I'm going to go try it out and hopefully I get the right answer.

Answer 21

you can do it! :)

Answer 22

but i'm here if you need any other assistance

Answer 23

Thank you. :)

Answer 24

did you get it already?

Answer 25

Yup. It's all good. :D

Answer 26

awesome stuff! :)