Is rationalizing the denominator an option

[Justabeginner]

Homework Statement

Evaluate x-> 3 for (x^3-27)/(x-3) by as many methods as you can think of.

Homework Equations

The Attempt at a Solution

I could only think of one:

1) (x-3)(x^2+3x+9)/(x-3)= (x^2+3x+9)
3^2 + 3(3) + 9= 27

What other methods can I do? Is rationalizing the denominator an option, even if it is redundant? Thank you.

 

[Dick]

Homework Statement

Evaluate x-> 3 for (x^3-27)/(x-3) by as many methods as you can think of.

Homework Equations

The Attempt at a Solution

I could only think of one:

1) (x-3)(x^2+3x+9)/(x-3)= (x^2+3x+9)
3^2 + 3(3) + 9= 27

What other methods can I do? Is rationalizing the denominator an option, even if it is redundant? Thank you.

The denominators already rational. Do you know l'Hopital's rule?

 

[Justabeginner]

Yes, I do! Why didn't I think of that? Thank you very much.