How do you find the limit of # (|x| -1)/((x+1)x)# as x approaches -1? Calculus Limits Determining Limits Algebraically 1 Answer Cesareo R. Jul 2, 2016 #lim_{x->-1} (|x| -1)/((x+1)x) =1# Explanation: # (|x| -1)/((x+1)x) = abs(x)/x cdot 1/(x+1)-1/(x(x+1))# for #x# near #-1# we have #abs(x)/x = -1# so, always near #-1# #-1/(x+1)-1/(x(x+1)) = -x/(x(x+1))-1/(x(x+1)) =-(x+1)/(x(x+1))=-1/x# then #lim_{x->-1} (|x| -1)/((x+1)x) =lim_{x->-1}-1/x=1# Answer link Related questions How do you find the limit #lim_(x->5)(x^2-6x+5)/(x^2-25)# ? How do you find the limit #lim_(x->3^+)|3-x|/(x^2-2x-3)# ? How do you find the limit #lim_(x->4)(x^3-64)/(x^2-8x+16)# ? How do you find the limit #lim_(x->2)(x^2+x-6)/(x-2)# ? How do you find the limit #lim_(x->-4)(x^2+5x+4)/(x^2+3x-4)# ? How do you find the limit #lim_(t->-3)(t^2-9)/(2t^2+7t+3)# ? How do you find the limit #lim_(h->0)((4+h)^2-16)/h# ? How do you find the limit #lim_(h->0)((2+h)^3-8)/h# ? How do you find the limit #lim_(x->9)(9-x)/(3-sqrt(x))# ? How do you find the limit #lim_(h->0)(sqrt(1+h)-1)/h# ? See all questions in Determining Limits Algebraically Impact of this question 1252 views around the world You can reuse this answer Creative Commons License