So Far I found the limit:

Lim x->0 1/(x+1)=1

then this is the scratchwork:

1/(x+1)-1<E when 0< |x-0|< delta

Not sure if I did this inequality right:

|1/(x+1)-1|<E <==>|x/(x+1)|<E <==> |x/(x+1)|< 0E??

Do I have to find a number M??

1/|x+1| less than or equal to M

Proof:

|1/(x+1)-1|=|x|/|x+1| then I don't know how to keep going, not sure if it's 0E is correct