document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=785183>Question 785183</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Change the rational equation to quadratic form and solve it by the most efficient method. (Enter your answers as a comma-separated list.)<BR>\n" );
document.write( " <BR>\n" );
document.write( "1<BR>\n" );
document.write( "x &#8722; 1<BR>\n" );
document.write( " + <BR>\n" );
document.write( "1<BR>\n" );
document.write( "x &#8722; 5<BR>\n" );
document.write( " = <BR>\n" );
document.write( "3<BR>\n" );
document.write( "8<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #477759 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=477759\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Maybe the question was<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28x-1%29%2B1%2F%28x-5%29=3%2F8 ALIGN=MIDDLE  ALT=\"1%2F%28x-1%29%2B1%2F%28x-5%29=3%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > which can be typed as 1/(x-1)+1/(x-5)=3/8<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28x-1%29%2B1%2F%28x-5%29=3%2F8 ALIGN=MIDDLE  ALT=\"1%2F%28x-1%29%2B1%2F%28x-5%29=3%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiplying both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%28x-1%29%28x-5%29 ALIGN=MIDDLE  ALT=\"8%28x-1%29%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to eliminate all denominators, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%28x-1%29%28x-5%29%281%2F%28x-1%29%2B1%2F%28x-5%29%29=8%28x-1%29%28x-5%29%283%2F8%29 ALIGN=MIDDLE  ALT=\"8%28x-1%29%28x-5%29%281%2F%28x-1%29%2B1%2F%28x-5%29%29=8%28x-1%29%28x-5%29%283%2F8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%28x-1%29%28x-5%29%2F%28x-1%29%2B8%28x-1%29%28x-5%29%2F%28x-5%29=8%28x-1%29%28x-5%293%2F8 ALIGN=MIDDLE  ALT=\"8%28x-1%29%28x-5%29%2F%28x-1%29%2B8%28x-1%29%28x-5%29%2F%28x-5%29=8%28x-1%29%28x-5%293%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%28x-5%29%2B8%28x-1%29=3%28x-1%29%28x-5%29 ALIGN=MIDDLE  ALT=\"8%28x-5%29%2B8%28x-1%29=3%28x-1%29%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x-40%2B8x-8=3%28x%5E2-6x%2B5%29 ALIGN=MIDDLE  ALT=\"8x-40%2B8x-8=3%28x%5E2-6x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x-48=3x%5E2-18x%2B15 ALIGN=MIDDLE  ALT=\"16x-48=3x%5E2-18x%2B15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=3x%5E2-18x%2B15-16x%2B48 ALIGN=MIDDLE  ALT=\"0=3x%5E2-18x%2B15-16x%2B48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-34x%2B63=0 ALIGN=MIDDLE  ALT=\"3x%5E2-34x%2B63=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Armed with a calculator, using the quadratic formula is the most efficient method.<BR>\n" );
document.write( "(With only pencil and paper, I would try factoring or completeing the square).<BR>\n" );
document.write( "Since the answer was obviously formatted to be entered into a computer directly, a calculator (or equivalent) was available.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+%28-%28-34%29+%2B-+sqrt%28%28-34%29%5E2-4%2A3%2A63+%29%29%2F%282%2A3%29+ ALIGN=MIDDLE  ALT=\"x=+%28-%28-34%29+%2B-+sqrt%28%28-34%29%5E2-4%2A3%2A63+%29%29%2F%282%2A3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+%2834+%2B-+sqrt%281156-756%29%29%2F6 ALIGN=MIDDLE  ALT=\"x=+%2834+%2B-+sqrt%281156-756%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+%2834+%2B-+sqrt%28400%29%29%2F6 ALIGN=MIDDLE  ALT=\"x=+%2834+%2B-+sqrt%28400%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+%2834+%2B-+20%29%2F6 ALIGN=MIDDLE  ALT=\"x=+%2834+%2B-+20%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The solutions are:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=+%2834+-+20%29%2F6=14%2F6=highlight%287%2F3%29 ALIGN=MIDDLE  ALT=\"x%5B1%5D=+%2834+-+20%29%2F6=14%2F6=highlight%287%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=+%2834+%2B+20%29%2F6=54%2F6=highlight%289%29 ALIGN=MIDDLE  ALT=\"x%5B1%5D=+%2834+%2B+20%29%2F6=54%2F6=highlight%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "I would enter the answers as 7/3,9 and hope the computer accepts that.<BR>\n" );
document.write( "{Format can be an issue for some small scale online courses). </SPAN>\n" );
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