document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=60985>Question 60985</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hopefully someone can help me with this one.  Thanks!\r<BR>\n" );
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document.write( "x / x-2 = 2/x-3  we are solving for x.\r<BR>\n" );
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document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #41900 by </B><A HREF=/tutors/aboutme.mpl?userid=joyofmath><B>joyofmath(189)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=joyofmath><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=41900\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28x-2%29+=+2%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"x%2F%28x-2%29+=+2%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiple both sides by <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;\" ><BR>\n" );
document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x-3%29%2F%28x-2%29+=+2 ALIGN=MIDDLE  ALT=\"x%28x-3%29%2F%28x-2%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now multiply both sides by <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;\" ><BR>\n" );
document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x-3%29+=+2%28x-2%29 ALIGN=MIDDLE  ALT=\"x%28x-3%29+=+2%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides out.<BR>\n" );
document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3x+=+2x-4 ALIGN=MIDDLE  ALT=\"x%5E2-3x+=+2x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 2x from both sides.<BR>\n" );
document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-5x+=+-4 ALIGN=MIDDLE  ALT=\"x%5E2-5x+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now add 4 to both sides.<BR>\n" );
document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-5x%2B4+=+0 ALIGN=MIDDLE  ALT=\"x%5E2-5x%2B4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This is a quadratic equation which factors:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%28x-4%29+=+0 ALIGN=MIDDLE  ALT=\"%28x-1%29%28x-4%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > are the two solutions.\r<BR>\n" );
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document.write( "To verify, plug 1 and 4 into the original equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28x-2%29+=+2%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"x%2F%28x-2%29+=+2%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%281-2%29+=+-1 ALIGN=MIDDLE  ALT=\"1%2F%281-2%29+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is indeed equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%28-2%29 ALIGN=MIDDLE  ALT=\"2%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F%284-2%29+=+4%2F2+=+2 ALIGN=MIDDLE  ALT=\"4%2F%284-2%29+=+4%2F2+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is indeed equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%284-3%29 ALIGN=MIDDLE  ALT=\"2%2F%284-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which = 2 </SPAN>\n" );
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