document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=181768>Question 181768</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/1602773033/algebrahomeworkh>saxon algebra 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Identify any excluded values.  Then simplify the expression.\r<BR>\n" );
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document.write( "9x^3-27x^2 over 12x-36\r<BR>\n" );
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document.write( "I identified the excluded value as x=3.<BR>\n" );
document.write( "I don't know what to do from here. Help! </SPAN>\n" );
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document.write( "You have correctly identified the excluded value, namely 3.\r<BR>\n" );
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document.write( "Now you need to factor both the numerator and denominator expressions.\r<BR>\n" );
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document.write( "In the numerator you have at least two factors of 3 in each term (or one factor of 9, if you prefer) and at least two factors of <i>x</i> in each term.  In the denominator, you have one factor of 12 in each term.  So:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math \frac{9x^3 - 27x^2}{12x - 36} = \frac{9x^2(x - 3)}{12(x - 3)}\">\r<BR>\n" );
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document.write( "Now you can eliminate the factor of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x - 3\"> common to both numerator and denominator to leave you with:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math \frac{9x^3 - 27x^2}{12x - 36} = \frac{9x^2(x - 3)}{12(x - 3)} = \frac {9x^2}{12} = \frac {3x^2}{4}\">\r<BR>\n" );
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document.write( "which is true if and only if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x \neq 3\">\r<BR>\n" );
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document.write( "It is important to note that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{9x^3 - 27x^2}{12x - 36} \neq  \frac {3x^2}{4}\"> if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x = 3\">\r<BR>\n" );
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document.write( "That's because if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x = 3\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac {3x^2}{4} = \frac {27}{4}\"> while <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{9x^3 - 27x^2}{12x - 36} \"> is undefined.\r<BR>\n" );
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document.write( "If you graph <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y = \frac{9x^3 - 27x^2}{12x - 36} \">, you would get something that looks very much like a parabola with vertex at the origin, but there would be a hole in the graph at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (3,\frac{27}{4})\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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