Evaluate the limit - Answer is -1/9 But I Don't Know How to Get It

Question

lim (1/a-1/3) /a-3

a(->)3

Answer 1

Emma,

I guess, the question must be on (1/a-1/3) /(a-3) not on (1/a-1/3) /a-3

Assuming that,

Let's first add fractions in the parenthesis

(1/a-1/3)=(3-a)/3a=-(a-3)/3a

Then divide the result on (a-3)

-((a-3)/3a)/(a-3)=-1/(3a) Therefore the limit is -1/9 when a->3

Hope it helps

A.B.