SOLUTION: What numbers should be excluded as values of x in the polynomial? x^2-4x+4 --------- x^2-5x+6

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: What numbers should be excluded as values of x in the polynomial? x^2-4x+4 --------- x^2-5x+6      Log On


   

Question 347727: What numbers should be excluded as values of x in the polynomial?
x^2-4x+4
---------
x^2-5x+6
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E2-4x%2B4%29%2F%28x%5E2-5x%2B6%29
The number to be excluded are those, if any, that make the denominator zero. This is so because we can never allow a division by zero!

The numbers that make the denominator zero those that are solutions to:
x%5E2-5x%2B6+=+0
To find the solutions to this quadratic equation we start by factoring:
%28x-2%29%28x-3%29+=+0
From 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:
x-2 = 0 oe x-3 = 0
Solving these we get:
x = 2 or x = 3.
These are the numbers which must be excluded as values of x (because they make the denominator zero).