document.write( "Question 352690: Find all numbers fro which the rational expression is undefined.\r
\n" ); document.write( "\n" ); document.write( "(r^3-9r)/(r^2-9) \n" ); document.write( "

Algebra.Com's Answer #252088 by jsmallt9(3758) $\"\"$ $\"About$

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$\"%28r%5E3-9r%29%2F%28r%5E2-9%29\"$
\n" ); document.write( "This expression will be undefined when the denominator is zero. So to find the numbers that will make the denominator zero we solve:
\n" ); document.write( " $\"r%5E2-9+=+0\"$
\n" ); document.write( "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 $\"a%5E2+-+b%5E2+=+%28a%2Bb%29%28a-b%29\"$ :
\n" ); document.write( " $\"%28r%2B3%29%28r-3%29+=+0\"$
\n" ); document.write( "From the Zero Product Property we know that this (or any) product is zero only if one (or more) of the factors is zero. So:
\n" ); document.write( "r + 3 = 0 or r - 3 = 0
\n" ); document.write( "Solving these we get:
\n" ); document.write( "r = -3 or r = 3
\n" ); document.write( "These are the values for r that will make the denominator zero and, therefore, the expression undefined. \n" ); document.write( "

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