How do you find the limit of (x-5)/(x^2-25)x−5x2−25 as x->5x→5? Calculus Limits Determining Limits Algebraically 1 Answer Alberto P. Oct 28, 2016 1/10110 Explanation: (x-5)/(x^2-5)=(x-5)/((x-5)(x+5))=1/(x+5), " for each " x!=5x−5x2−5=x−5(x−5)(x+5)=1x+5, for each x≠5 so lim_(x->5) f(x) = lim_(x->5) 1/(x+5) = 1/10 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 2475 views around the world You can reuse this answer Creative Commons License