document.write( "Question 1100446: Where is the hole of the following found: x^2+3x-4/x^2-x-20.\r
\n" ); document.write( "\n" ); document.write( "(I have to do several of these and the book is confusing. Asking for help with this one so I can continue on with others. Thank you) \n" ); document.write( "

Algebra.Com's Answer #714933 by Edwin McCravy(20081) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Factor the top and bottom:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now as long as you do not cancel the (x+4)'s, then\r\n" );
document.write( "x cannot equal to -4, because if you substitute\r\n" );
document.write( "x = -4, you get:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "That is undefined, because we cannot divide anything\r\n" );
document.write( "by 0, not even 0 divided by 0.  It's simply undefined.\r\n" );
document.write( "That's what causes the hole to be in the graph.\r\n" );
document.write( "\r\n" );
document.write( "Now if we cancel the (x+4)'s we get a graph which has\r\n" );
document.write( "no hole.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Its graph does NOT have a hole!\r\n" );
document.write( "\r\n" );
document.write( "Notice that if we substitute x=-4 in it, we get:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So the graph goes through the point \r\n" );
document.write( "\r\n" );
document.write( "So the graph of\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "whih has no hole, is this:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "That's the graph WITHOUT the hole because the point  is there, indicated by \r\n" );
document.write( "the darkened circle.\r\n" );
document.write( "\r\n" );
document.write( "Now let's go back to the original equation, which has a hole,\r\n" );
document.write( "because the (x+4)'s were not canceled:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Its graph is the same as the graph of  except\r\n" );
document.write( "that it has a hole and doesn't go through the point . Its graph is:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So when you leave the equation as it was given originally,\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "And do not factor and cancel out the (x+4)'s then you have a\r\n" );
document.write( "hole at the point that makes (x+4) equal to 0. \r\n" );
document.write( "\r\n" );
document.write( "Then when you factor and cancel the (x+4)'s, you \"fill in\" the \r\n" );
document.write( "hole.  There is a hole when you don't cancel, and no hole when\r\n" );
document.write( "you do cancel.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \n" ); document.write( "

\n" );