document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206908>Question 1206908</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the equation of a possible rational function given the following information. Leave in factored form.<BR>\n" );
document.write( "Vertical asymptote x = 2, discontinuous point (−3, −4/5), x  -  intercept at x = −5 and horizontal asymptote at y = 2. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844651 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=844651\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a rational function :\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29+=+a%2Ap%28x%29+%2Fq%28x%29+ ALIGN=MIDDLE  ALT=\"R%28x%29+=+a%2Ap%28x%29+%2Fq%28x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29 ALIGN=MIDDLE  ALT=\"p%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%28x%29 ALIGN=MIDDLE  ALT=\"q%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are both polynomials\r<BR>\n" );
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document.write( "given:\r<BR>\n" );
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document.write( "Vertical asymptote <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2 ALIGN=MIDDLE  ALT=\"x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >: value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > that makes denominator equal to zero , so\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%28x%29=%28x-2%29 ALIGN=MIDDLE  ALT=\"q%28x%29=%28x-2%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=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > - intercept at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-5 ALIGN=MIDDLE  ALT=\"x+=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >=>numerator is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29=a%28x%2B5%29 ALIGN=MIDDLE  ALT=\"p%28x%29=a%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so far <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29=a%28x%2B5%29%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"R%28x%29=a%28x%2B5%29%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " horizontal asymptote at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the highest power of numerator and denominator are same and coefficient of numerator is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > times that of denominator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29=2%28x%2B5%29%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"R%28x%29=2%28x%2B5%29%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "discontinuous point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2F5 ALIGN=MIDDLE  ALT=\"-4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "check given point\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2F5=2%28-3%2B5%29%2F%28-3-2%29 ALIGN=MIDDLE  ALT=\"-4%2F5=2%28-3%2B5%29%2F%28-3-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> true\r<BR>\n" );
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document.write( "=>for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, denominator will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=zero ALIGN=MIDDLE  ALT=\"zero\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29 ALIGN=MIDDLE  ALT=\"%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both, numerator and denominator, and your equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29+=+2%28%28x%2B5%29%28x%2B3%29%29%2F%28%28x-2%29%28x%2B3%29%29 ALIGN=MIDDLE  ALT=\"R%28x%29+=+2%28%28x%2B5%29%28x%2B3%29%29%2F%28%28x-2%29%28x%2B3%29%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=+drawing%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+20%2C%0D%0Acircle%28-3%2C-4%2F5%2C.12%29%2C+locate%28-3%2C-4%2F5%2Cp%28-3%2C-4%2F5%29%29%2C%0D%0Acircle%28-5%2C0%2C.12%29%2C+locate%28-5%2C0.7%2Cp%28-5%2C0%29%29%2C%0D%0Ablue%28line%282%2C20%2C2%2C-10%29%29%2C%0D%0Agraph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+20%2C+2%28%28x%2B5%29%28x%2B3%29%29%2F%28%28x-2%29%28x%2B3%29%29%2C2%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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