Elipson-delta definition of limit

[layd33foxx]

lim x->0 1/(x+1)

I did some work but after that I don't know how to keep going.
if 0<|x-c|<delta => |f(x)-<E|, then lim x->c f(x)=L
0<|x-0|<delta=> |1/(x+1)-1|
scratchwork: |1/(x+1)-1|<E
|x/x+1|<E
|x|/|x+1|<E
|x|<|x+1|E
restrict |x|<1/2
-1/2<x<1/2=>1/2<x+1<3/2=>1/2 <|x+1|
|x|<|x+1|E
|x|<1/2 E
delta=min{1/2,1/2E}
proof ??