document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=790553>Question 790553</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 16 / (x+2) = 1 + 2/(x-4)\r<BR>\n" );
document.write( "\n" );
document.write( "I first eliminated the denominator x+2, then the denominator x-4.  Simplifying and setting equal to 0, I get x = -6, -10.  These solutions do not work, but their positives do.  I don't understand how to solve this equation without getting negative values for x.\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks in advance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #479303 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=479303\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I get 6 and 10.<BR>\n" );
document.write( "You must have made some small mistake.<BR>\n" );
document.write( "It is very hard to notice one's own mistakes.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16+%2F+%28x%2B2%29+=+1+%2B+2%2F%28x-4%29 ALIGN=MIDDLE  ALT=\"16+%2F+%28x%2B2%29+=+1+%2B+2%2F%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiplying both sides times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%28x-4%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > I get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%28x%2B2%29%28x-4%29%2F+%28x%2B2%29+=+%28x%2B2%29%28x-4%29+%2B+2%28x%2B2%29%28x-4%29%2F%28x-4%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%28x-4%29+=+%28x%2B2%29%28x-4%29+%2B+2%28x%2B2%29 ALIGN=MIDDLE  ALT=\"16%28x-4%29+=+%28x%2B2%29%28x-4%29+%2B+2%28x%2B2%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-64+=+x%5E2-2x-8+%2B+2x%2B4 ALIGN=MIDDLE  ALT=\"16x-64+=+x%5E2-2x-8+%2B+2x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x-64+=+x%5E2+-8+%2B4 ALIGN=MIDDLE  ALT=\"16x-64+=+x%5E2+-8+%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x-64+=+x%5E2-4 ALIGN=MIDDLE  ALT=\"16x-64+=+x%5E2-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+x%5E2-4-16x%2B64 ALIGN=MIDDLE  ALT=\"0+=+x%5E2-4-16x%2B64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-16x%2B60=0 ALIGN=MIDDLE  ALT=\"x%5E2-16x%2B60=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factoring, I get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-6%29%28x-10%29=0 ALIGN=MIDDLE  ALT=\"%28x-6%29%28x-10%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, either <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-6=0 ALIGN=MIDDLE  ALT=\"x-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=6%29 ALIGN=MIDDLE  ALT=\"highlight%28x=6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-10=0 ALIGN=MIDDLE  ALT=\"x-10=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=10%29 ALIGN=MIDDLE  ALT=\"highlight%28x=10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " <BR>\n" );
document.write( "If you do not like factoring, you could use the quadratic formula, or \"complete the square\" instead.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Completing the square:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-16x%2B60=0 ALIGN=MIDDLE  ALT=\"x%5E2-16x%2B60=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-16x=-60 ALIGN=MIDDLE  ALT=\"x%5E2-16x=-60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-16x%2B64=-60%2B64 ALIGN=MIDDLE  ALT=\"x%5E2-16x%2B64=-60%2B64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-8%29%5E2=4 ALIGN=MIDDLE  ALT=\"%28x-8%29%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So either <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-8=2 ALIGN=MIDDLE  ALT=\"x-8=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%2B8 ALIGN=MIDDLE  ALT=\"x=2%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=10%29 ALIGN=MIDDLE  ALT=\"highlight%28x=10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-8=-2 ALIGN=MIDDLE  ALT=\"x-8=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2%2B8 ALIGN=MIDDLE  ALT=\"x=-2%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=6%29 ALIGN=MIDDLE  ALT=\"highlight%28x=6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "Using the quadratic formula:<BR>\n" );
document.write( "The solutions to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > are given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "In the case of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-16x%2B60=0 ALIGN=MIDDLE  ALT=\"x%5E2-16x%2B60=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-16 ALIGN=MIDDLE  ALT=\"b=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=60 ALIGN=MIDDLE  ALT=\"c=60\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-16%29+%2B-+sqrt%28%28-16%29%5E2-4%2A1%2A60+%29%29%2F%282%2A1%29+=%2816+%2B-+sqrt%28256-240%29%29%2F2=%2816+%2B-+sqrt%2816%29%29%2F2=%2816+%2B-+4%29%2F2 ALIGN=MIDDLE   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=%2816+%2B+4%29%2F2=20%2F2=highlight%28x=10%29 ALIGN=MIDDLE  ALT=\"x=%2816+%2B+4%29%2F2=20%2F2=highlight%28x=10%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=x=%2816+-+4%29%2F2=12%2F2=highlight%28x=6%29 ALIGN=MIDDLE  ALT=\"x=%2816+-+4%29%2F2=12%2F2=highlight%28x=6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );