Finding a limit without l'hopial

[tglover]

Homework Statement

lim x→2 ((sqrt(6-x)-2) / (sqrt(3-x) - 1)

Homework Equations

none

The Attempt at a Solution

My daughter's grade 12 mathematics class is not yet using l'hopital, yet this question has been posed as a practice question. I can solve it readily with l'hopital, however without it I'm stumped. When I attempt by multiplying numerator and denominator by (sqrt(3-x) +1 ) predictably I get 0 for my troubles.

 

[dynamicsolo]

The attachment is lost now, but this thread had the same limit problem: https://www.physicsforums.com/showthread.php?t=542547

(You are on the right path, but you need to take it further...)