Question

Find the limit as x approaches -3 of (x+3)/(x+2)^2-1

Answer 1

i know the answer is -1/2 but i do not understand how?? i keep getting the denominator as either positive two or negative three

Answer 2

\[\lim_{x \rightarrow -3}(\frac{x+3}{(x+2)^2}-1)\]
we can find this limit by direct substitution

Answer 3

or did you mean (x+3)/((x+2)^2-1) ?

Answer 4

if so try to fact the denominator

Answer 5

the -1 is in the denominator

Answer 6

i did and i canceled out the (x+3) and am left with (x+2)-1

Answer 7

not sure how to go on from here

Answer 8

you do know (x+2)^2 is x^2+4x+4 right?

Answer 9

and that x^2+4x+4-1
is the same as x^2+4x+3
can you continue ?

Answer 10

yes and you factor it to get (x+3)(x+1)

Answer 11

right?

Answer 12

ok cancel out the common factor

Answer 13

\[\frac{\cancel{(x+3)}}{\cancel{(x+3)}(x+1)}\]

Answer 14

okay i got it thank you so much!!