SOLUTION: Which value(s) of x should be excluded for the polynomial? x^2-16 ------ x^2-6x+9

Question 347458: Which value(s) of x should be excluded for the polynomial?
x^2-16
------
x^2-6x+9
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Your expression is not a polynomial. It is a rational expression (ratio of polynomials).

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?

So you just have to find the x value(s) that make your denominator zero. That is, solve:

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

By the Zero Product Property we know that this (or any) product can be zero only 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.
RELATED QUESTIONS
What number(s) should be excluded as values of x in the polynomial? x+2 -----... (answered by ankor@dixie-net.com)

What numbers should be excluded as values of x in the polynomial? x^2-4x+4 ---------... (answered by jsmallt9)

What is the excluded value of x for the polynomial expression: \ 2x-4 _____... (answered by jim_thompson5910)

Determine the value(s) of the variable that must be excluded from the domain. f(x) =... (answered by Edwin McCravy)

Determine the value(s) of the variable that must be excluded from the domain. (x^2 -... (answered by josgarithmetic)

X^2+7x-18 -------------- X^2-11x+18 Determine what value(s) if any, of the variable... (answered by josgarithmetic)

Find the excluded value(s) for the following expression : 4x -----... (answered by jsmallt9)

Find the excluded value(s) for the following expression :... (answered by tommyt3rd)

Give the excluded value(s) for the fraction... (answered by ewatrrr)