document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=185346>Question 185346</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This question is on Rational Expressions, and solving them using the Algebraic method to find the vertical asymptote.\r<BR>\n" );
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document.write( "g(x)=(x^2+x+1)/(5x^2+1)  I can't figure out where to start...\r<BR>\n" );
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document.write( "Also simplifying (3a^2-6a)/(12-6a)   What the heck is this? And where do I start and finish this crazy problem??? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #139021 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=139021\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> # 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=%28x%5E2%2Bx%2B1%29%2F%285x%5E2%2B1%29 ALIGN=MIDDLE  ALT=\"g%28x%29=%28x%5E2%2Bx%2B1%29%2F%285x%5E2%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2%2B1=0 ALIGN=MIDDLE  ALT=\"5x%5E2%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set the denominator equal to zero. Remember, vertical asymptotes arise only when there's a division by zero\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2=-1 ALIGN=MIDDLE  ALT=\"5x%5E2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 1 from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=-1%2F5 ALIGN=MIDDLE  ALT=\"x%5E2=-1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%28-1%2F5%29 ALIGN=MIDDLE  ALT=\"x=sqrt%28-1%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides.\r<BR>\n" );
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document.write( "Remember, you CANNOT take the square root of a negative number. So this means that the value of \"x\" will be complex/imaginary. \r<BR>\n" );
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document.write( "In other words, there is NO value of \"x\" that will make the denominator zero. \r<BR>\n" );
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document.write( "So there are no vertical asymptotes (graph the function to verify)\r<BR>\n" );
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document.write( "# 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283a%5E2-6a%29%2F%2812-6a%29 ALIGN=MIDDLE  ALT=\"%283a%5E2-6a%29%2F%2812-6a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283a%28a-2%29%29%2F%2812-6a%29 ALIGN=MIDDLE  ALT=\"%283a%28a-2%29%29%2F%2812-6a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the numerator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283a%28a-2%29%29%2F%28-6%28a-2%29%29 ALIGN=MIDDLE  ALT=\"%283a%28a-2%29%29%2F%28-6%28a-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the denominator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28a%28a-2%29%29%2F%282%28a-2%29%29 ALIGN=MIDDLE  ALT=\"-%28a%28a-2%29%29%2F%282%28a-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F%28-6%29 ALIGN=MIDDLE  ALT=\"3%2F%28-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the outer coefficients) to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2 ALIGN=MIDDLE  ALT=\"-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28a%2Ahighlight%28%28a-2%29%29%29%2F%282%2Ahighlight%28%28a-2%29%29%29 ALIGN=MIDDLE  ALT=\"-%28a%2Ahighlight%28%28a-2%29%29%29%2F%282%2Ahighlight%28%28a-2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Highlight the common terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28a%2Across%28%28a-2%29%29%29%2F%282%2Across%28%28a-2%29%29%29 ALIGN=MIDDLE  ALT=\"-%28a%2Across%28%28a-2%29%29%29%2F%282%2Across%28%28a-2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel out the common terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%2F2 ALIGN=MIDDLE  ALT=\"-a%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283a%5E2-6a%29%2F%2812-6a%29 ALIGN=MIDDLE  ALT=\"%283a%5E2-6a%29%2F%2812-6a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%2F2 ALIGN=MIDDLE  ALT=\"-a%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283a%5E2-6a%29%2F%2812-6a%29=-a%2F2 ALIGN=MIDDLE  ALT=\"%283a%5E2-6a%29%2F%2812-6a%29=-a%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%3C%3E2 ALIGN=MIDDLE  ALT=\"a%3C%3E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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