Question

Determine the simplified form for the slope of the tangent at any point for the function p(x)=1/x+1

Answer 1

For some weird reason I will assume you meant
p(x) = 1/(x + 1)
p(x+h) = 1/(x+h+1)
slope of tangent at any point
= lim ( p(x+h) - p(x) )/h , as h ----> 0
= lim (1/(x+h+1) - 1/(x+1) )/h
= lim ( x+1 - x - h - 1)/((x+1)(x+h+1) ) / h
= lim ( -h/((x+1)(x+h+1) ) / h
= lim -1/((x+1)(x+h+1) , as h ---> 0
= -1/(x+1)^2

If you meant it the way you typed it, then just make the necessary changes.

Answer 2

Sorry I meant 1/(x + 1), thank you very much for your help!!!