document.write( "Question 347727: What numbers should be excluded as values of x in the polynomial?
\n" ); document.write( "x^2-4x+4
\n" ); document.write( "---------
\n" ); document.write( "x^2-5x+6 \n" ); document.write( "

Algebra.Com's Answer #248753 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"%28x%5E2-4x%2B4%29%2F%28x%5E2-5x%2B6%29\"$
\n" ); document.write( "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!

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

\n" );