document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=893508>Question 893508</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve<BR>\n" );
document.write( "H(x)= 8x over x(x^2-49) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #541354 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=541354\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> That is a rational function.  Nothing to solve.  What do you really want from it?  What is x?  What is H(x) for some given x?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28H%28x%29=%288x%29%2F%28x%28x%5E2-49%29%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28H%28x%29=%288x%29%2F%28x%28x%5E2-49%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "It EXCLUDES any value if x=0, because H is undefined for x=0.<BR>\n" );
document.write( "It has a vertical asymptotes for x=-7 and x=7, because H is undefined at those values.<BR>\n" );
document.write( "H contains the factor, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fx ALIGN=MIDDLE  ALT=\"x%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is why x=0 is a hole, and not an asymptote.\r<BR>\n" );
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document.write( "You can check the signs of H around the critical x values so you can find where H is<BR>\n" );
document.write( "positive and where negative, and how H behaves around the asymptote.  The critical values<BR>\n" );
document.write( "of x are 0 and -7 and 7.\r<BR>\n" );
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document.write( "(This attempted graph is not rendering.  Try putting the function either into a graphing calculator or in the text search field of google.)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-12%2C12%2C-10%2C10%2C%288x%29%2F%28x%28x%5E2-49%29%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-12%2C12%2C-10%2C10%2C%288x%29%2F%28x%28x%5E2-49%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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