What is the limit of # [(x^2) + 5x + 4] / [(x^2) + 3x -4]# as x approaches -4? Calculus Limits Determining Limits Algebraically 1 Answer Ratnaker Mehta Feb 2, 2017 #3/5.# Explanation: #"The Nr.="x^2+5x-4=(x+4)(x+1).# #"The Dr.="x^2+3x-4=(x+4)(x-1)#. Therefore, the Limit#=lim_(x to -4) {(cancel(x+4))(x+1)}/{(cancel(x+4))(x-1)}# #=lim_(x to -4) (x+1)/(x-1)# #=(-4+1)/(-4-1)=(-3)/(-5)# #=3/5#. 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 9987 views around the world You can reuse this answer Creative Commons License