Question

Question #dc253

Answer 1

By eliminating common factors, we can find
`lim_{a to 0}{(a-3)^2-9}/a=-6`.

Let us look at some details.

First, we notice that both the numerator and the denominator approach `0` as `a` approaches `0`, which indicates that they share a common factor `a`.

`lim_{a to 0}{(a-3)^2-9}/a`

by multiplying out the square,

`=lim_{a to 0}{a^2-6a+9-9}/a`

by cancelling out the 9's,

`=lim_{a to 0}{a^2-6a}/a`

by factoring out `a`,

`=lim_{a to 0}{a(a-6)}/a`

by cancelling `a`'s,

`=lim_{a to 0}(a-6)`

by plugging in `a=0`,

`=0-6=-6`