document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=77043>Question 77043</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the numbers excluded from the domain.   \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28X%29=+%28x-2%29%2F%284x%5E2-5x-6%29 ALIGN=MIDDLE  ALT=\"f%28X%29=+%28x-2%29%2F%284x%5E2-5x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "a.) -2, 4/3    B.) 2, -4/3    c.) -2, 3/4   d.)  2, -3/4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #55225 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=55225\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28X%29=+%28x-2%29%2F%284x%5E2-5x-6%29 ALIGN=MIDDLE  ALT=\"f%28X%29=+%28x-2%29%2F%284x%5E2-5x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "Factor the denominator on the right side.  You will have to play with this a while, but<BR>\n" );
document.write( "without going into the process of factoring, I'll tell you that the denominator factors into<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%2A%284x%2B3%29 ALIGN=MIDDLE  ALT=\"%28x-2%29%2A%284x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute this as the denominator in the original equation and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28X%29=+%28x-2%29%2F%28%28x-2%29%2A%284x%2B3%29%29 ALIGN=MIDDLE  ALT=\"f%28X%29=+%28x-2%29%2F%28%28x-2%29%2A%284x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "Now recognize that the rules of algebra do not allow dividing by zero.  Therefore, neither <BR>\n" );
document.write( "of the factors in the denominator can equal zero, because if either did equal zero, the<BR>\n" );
document.write( "denominator would be zero.<BR>\n" );
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document.write( "So you are not allowed to have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29=0 ALIGN=MIDDLE  ALT=\"%28x-2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Solve for x by adding 2 to both sides of<BR>\n" );
document.write( "this equation and you get x = +2.  So you cannot allow x to equal +2.<BR>\n" );
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document.write( "Next, the factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+%2B+3 ALIGN=MIDDLE  ALT=\"4x+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > also cannot equal zero.  So you are not allowed to have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+%2B+3+=+0 ALIGN=MIDDLE  ALT=\"4x+%2B+3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Subtract 3 from both sides and this reduces to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+=+-3 ALIGN=MIDDLE  ALT=\"4x+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then solve for x by dividing both sides by 4 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3%2F4 ALIGN=MIDDLE  ALT=\"x+=+-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So we cannot have x equal <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F4 ALIGN=MIDDLE  ALT=\"-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > either.  So the two value that x cannot be are +2 and<BR>\n" );
document.write( "-3/4.<BR>\n" );
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document.write( "Answer D is the correct choice.<BR>\n" );
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document.write( "Hope this helps you to understand that division by zero is one of the things to look for<BR>\n" );
document.write( "when you have an x term in the denominator because x cannot take any value that will cause<BR>\n" );
document.write( "a division by zero. <BR>\n" );
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