document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1028105>Question 1028105</A>: <I><SPAN STYLE=\"word-break: break-all;\"> First, Graph: f(x) =x^2+2/x^2+x-2\r<BR>\n" );
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document.write( "Then:\r<BR>\n" );
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document.write( "Identify Vertical Asymptotes:\r<BR>\n" );
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document.write( "Algebraic Verification:\r<BR>\n" );
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document.write( "Identify Horizontal Asymptotes:\r<BR>\n" );
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document.write( "Algebraic Verification:\r<BR>\n" );
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document.write( "Identify Oblique Asymptote:\r<BR>\n" );
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document.write( "Algebraic verification: </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #643288 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</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=643288\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) =x^2+2/x^2+x-2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=x%5E2%2B2%2Fx%5E2%2Bx-2 ALIGN=MIDDLE  ALT=\"f%28x%29+=x%5E2%2B2%2Fx%5E2%2Bx-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >   OR   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=%28x%5E2%2B2%29%2F%28x%5E2%2Bx-2%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=%28x%5E2%2B2%29%2F%28x%5E2%2Bx-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  ?\r<BR>\n" );
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document.write( "The second definition is assumed in this work.\r<BR>\n" );
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document.write( "First, here is the graph, simply applying the graphing code for the site:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-6%2C6%2C-6%2C6%2C%28x%5E2%2B2%29%2F%28x%5E2%2Bx-2%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-6%2C6%2C-6%2C6%2C%28x%5E2%2B2%29%2F%28x%5E2%2Bx-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Factorize numerator and denominator completely, at least for Real number purposes.\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%5E2%2B2%29%2F%28%28x-1%29%28x%2B2%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%5E2%2B2%29%2F%28%28x-1%29%28x%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "No hole since no factor is common between numerator and denominator.\r<BR>\n" );
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document.write( "Undefined for x=1 and x=-2, so this causes vertical asymptotes.\r<BR>\n" );
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document.write( "Degree of numerator and denominator both EVEN and EQUAL, so as x tends unbounded in either direction, f approaches 1.   Horizontal asymptote y=1.\r<BR>\n" );
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document.write( "Try polynomial long division.  You will find 1 plus some rational expression, consistant with what is found as the horizontal asymptote.  NO oblique asymptote! </SPAN>\n" );
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