document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=969518>Question 969518</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Im taking a course online, and I couldn't be more confused. There's no teacher, and I have no idea where to even start. If someone could show me the steps to solving these equations with the two examples I provided, I would really appreciate it. Thank you sooo much! \r<BR>\n" );
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document.write( "They ask me to simplify and state the restrictions on the variable. (dividing rational expressions)\r<BR>\n" );
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document.write( "1.      x^2-x-6 over x^2- 4   /   x^2-2x+1 over x^2-1 \r<BR>\n" );
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document.write( "2.  2x over 9x^2 +15x   -  8 over 3x + 5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #592386 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=592386\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> #2:\r<BR>\n" );
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document.write( "The best I can make of your description:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282x%29%2F%289x%5E2%2B15x-8%29%29%2F%283x%2B5%29 ALIGN=MIDDLE  ALT=\"%28%282x%29%2F%289x%5E2%2B15x-8%29%29%2F%283x%2B5%29\"   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=highlight_green%28%282x%29%2A%283x%2B5%29%2F%289x%5E2%2B15x-8%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28%282x%29%2A%283x%2B5%29%2F%289x%5E2%2B15x-8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "but WHAT do you want with it?  This is not an equation, so nothing to \"solve\".\r<BR>\n" );
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document.write( "Denominator: (3x 8)(3x 1)----none of these...<BR>\n" );
document.write( "(9x  8)(x  1)------none of these....<BR>\n" );
document.write( "<s>The denominator is apparently not factorable</s>.  (More combinations were checked than those shown).(Try checking the discriminant, since the graph below means that there ARE two vertical asymptotes.  This means, use general solution of quadratic formula to find zeros of the denominator.)\r<BR>\n" );
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document.write( "Your rational expression has two x-intercepts:  0 and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The degree of numerator and denominator both are two; so expect the leading terms of numerator and denominator to give unbound behavior of x to positive or negative infinity as   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286x%5E2%29%2F%289x%5E2%29=6%2F9=2%2F3 ALIGN=MIDDLE  ALT=\"%286x%5E2%29%2F%289x%5E2%29=6%2F9=2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or a horizontal asymptote of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%2F3 ALIGN=MIDDLE  ALT=\"y=2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "A few other details about the rational expression can also be examined.\r<BR>\n" );
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document.write( "Expect a graph like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-5%2C5%2C-5%2C5%2C%282x%29%2A%283x%2B5%29%2F%289x%5E2%2B15x-8%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-5%2C5%2C-5%2C5%2C%282x%29%2A%283x%2B5%29%2F%289x%5E2%2B15x-8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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