document.write( "Question 957461: If $\"m%28x%29=%285-x%29%2F%28x%5E2-25%29\"$ then at $\"x=5\"$ the graph\r
\n" ); document.write( "\n" ); document.write( "A. Has a vertical asymptote
\n" ); document.write( "B. Has an x-intercept
\n" ); document.write( "C. Has a hole at (5 , 1/10)
\n" ); document.write( "D. Has a hole at (5 , -1/10)
\n" ); document.write( "E. None of the above \n" ); document.write( "

Algebra.Com's Answer #585101 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "The denominator is not equal to 0:\r\n" );
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document.write( ", \r\n" );
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document.write( ", \r\n" );
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document.write( "So\r\n" );
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document.write( " where , \r\n" );
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document.write( "Get numerator in descending order:\r\n" );
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document.write( " where , \r\n" );
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document.write( "Factor out -1 in numerator, factor denominator:\r\n" );
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document.write( " where , \r\n" );
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document.write( "Now if we cancel the (x-5)'s we will have a slightly differen\r\n" );
document.write( "function, which does have a value at x=5, since the denominator will\r\n" );
document.write( "not be 0. Let's call it .  \r\n" );
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document.write( "There is an asymptote at x=-5 but not at x=5. \r\n" );
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document.write( "Notice that  does have a value at x=5, namely, \r\n" );
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document.write( "However the original problem  does not have\r\n" );
document.write( "a value  at x=5\r\n" );
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document.write( " and  are identical everywhere\r\n" );
document.write( "except at x=5.  So there is a hole in m(x) at the point (5,-1/10).  \r\n" );
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document.write( "Edwin

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