Question 352690
{{{(r^3-9r)/(r^2-9)}}}
This expression will be undefined when the denominator is zero. So to find the numbers that will make the denominator zero we solve:
{{{r^2-9 = 0}}}
To solve this we factor it (or use the Quadratic Formula). Since this is a difference of squares, this factors very easily according tothe pattern {{{a^2 - b^2 = (a+b)(a-b)}}}:
{{{(r+3)(r-3) = 0}}}
From the Zero Product Property we know that this (or any) product is zero <i>only</i> if one (or more) of the factors is zero. So:
r + 3 = 0  or r - 3 = 0
Solving these we get:
r = -3 or r = 3
These are the values for r that will make the denominator zero and, therefore, the expression undefined.