Question

lim (x ---> -1) (x^2+6x+5)/(x^2-3x-4)

Answer 1

can you factor the numerator and denominator ?

Answer 2

No :(

Answer 3

x^2+6x+5
think of 2 numbers whose product is +5 and sum is +6

Answer 4

it gets down to (-1+3)(-1+2)/(-1+1)(-1-4)

Answer 5

((-1+3)(-1+2))/((-1+1)(-1-4)) its undetermined

Answer 6

@Mertsj

Answer 7

@ganeshie8 @ajprincess

Answer 8

Factorization will work here..

For that you have to first learn how to factorize the things..

Answer 9

do u need explanation

Answer 10

L'Hopital :)

Answer 11

For numerator part:

\[x^2 + 6x + 5\]

See here : a = 1 here b= 6 here and c = 5 here by comparing it with \(ax^2 + bx + c\).

So, here we have to find factors of 5 that will add to 6 and product to 5.

So, by calculations in mind, I am getting +5 and +1.

So, this will go like:
\[x^2 + 6x + 5 \implies x^2 + x + 5x + 5 \implies x(x + 1) + 5(x + 1) \implies (x + 1)(x + 5)\]

Answer 12

See, you have found the factors correctly but why aren't you cancelling the common factors??

You got (x+1) on numerator and denominator both, just cancel them and then apply the limits..

Answer 13

\[\frac{(x + 5)\cancel{(x +1)}}{\cancel{(x + 1)} (x-4)} \implies \frac{(x+5)}{(x-4)}\]

Answer 14

And now apply the limits here..

Answer 15

I see!!

Answer 16

Oh, you can see??

Great...

I can also see...

Answer 17

-4/5

Answer 18

Good..