Find the limit of the function algebraically.

limit as x approaches five of quantity x squared minus twenty five divided by quantity x minus five.

Factor x^2 - 25 as

x^2-5^2

= (x+5) (x-5)

so,

(x^2-25) / (x-5) = (x+5) (x-5) / (x-5) = x+5

limit of x->5 of (x+5)

can be just found by plugging in x = 5.

lim x->5 (x+5) = 5+5 = 10.

so the limit value = 10