document.write( "Question 132142: 27) The numbers for which the rational expression is undefined are $\"%28r%5E3-7r%29%2F%28r%5E2-49%29\"$ \n" ); document.write( "

Algebra.Com's Answer #96517 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " $\"%28r%5E3-7r%29%2F%28r%5E2-49%29\"$ Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( " $\"r%5E2-49=0\"$ Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of r that make the denominator zero, then we must exclude them from the domain.\r
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\n" ); document.write( "\n" ); document.write( " $\"%28r-7%29%28r%2B7%29=0\"$ Factor the left side (note: if you need help with factoring, check out this solver)\r
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\n" ); document.write( "\n" ); document.write( "Now set each factor equal to zero:\r
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\n" ); document.write( "\n" ); document.write( " $\"r-7=0\"$ or $\"r%2B7=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"r=7\"$ or $\"r=-7\"$ Now solve for r in each case\r
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\n" ); document.write( "\n" ); document.write( "So our solutions are $\"r=7\"$ or $\"r=-7\"$ \r
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\n" ); document.write( "\n" ); document.write( "Since $\"r=-7\"$ and $\"r=7\"$ make the denominator equal to zero, this means $\"r=-7\"$ and $\"r=7\"$ make the rational expression undefined (remember you cannot divide by zero)\r
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