Question 347458
Your expression is not a polynomial. It is a rational expression (ratio of polynomials).<br>
The only rule in Math that has no exceptions is: Never divide by zero! Whenever you have a fraction, you must ensure that the denominator must not be zero. This is what your problem is asking. "Which value(s) of x should be excluded for the {rational expression]" because it/they would make the denominator zero?<br>
So you just have to find the x value(s) that make your denominator zero. That is, solve:
{{{x^2 -6x + 9 = 0}}}
and exclude these numbers.
To solve this equation we factor it (or use the Quadratic Formula). This factors fairly easily:
(x-3)(x-3) = 0
or
{{{(x-3)^2 = 0}}}
By the Zero Product Property we know that this (or any) product can be zero <i>only</i> if one (or more) of the factors is zero. So, since we have two identical factors, we just have to figure out the solution to
x-3 = 0
which is
x = 3
Three is the only number that will make the denominator zero. This is the only number that must be excluded as a value for x. So x can be any number except 3.