document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=984771>Question 984771</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if x = y+z, y = z+x, z = x+y, then what is the value of (1/(x+1)) + (1/(y+1)) + (1/(z+1))?\r<BR>\n" );
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document.write( "How to solve this? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #605601 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52786)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=605601\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "If &nbsp;x = y+z, &nbsp;y = z+x, &nbsp;z = x+y, &nbsp;then what is the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%28x%2B1%29%29 ALIGN=MIDDLE  ALT=\"%281%2F%28x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%28y%2B1%29%29 ALIGN=MIDDLE  ALT=\"%281%2F%28y%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%28z%2B1%29%29 ALIGN=MIDDLE  ALT=\"%281%2F%28z%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ?<BR>\n" );
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document.write( "You have the system of three linear equations with three unknowns\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x+-+y+-+z+=+0%2C%0D%0A-x+%2B+y+-+z+=+0%2C%0D%0A-x+-+y+%2B+z+=+0%29 ALIGN=MIDDLE  ALT=\"system%28x+-+y+-+z+=+0%2C%0D%0A-x+%2B+y+-+z+=+0%2C%0D%0A-x+-+y+%2B+z+=+0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Add all three equations. &nbsp;You will get\r<BR>\n" );
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document.write( "-x - y - z = 0, &nbsp;&nbsp;&nbsp;&nbsp;or\r<BR>\n" );
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document.write( "x + y + z = 0. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(*)\r<BR>\n" );
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document.write( "Now, &nbsp;add the last equation and the first one of the system. &nbsp;You will get\r<BR>\n" );
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document.write( "2x = 0, &nbsp;&nbsp;and, &nbsp;&nbsp;hence, &nbsp;&nbsp;x = 0.\r<BR>\n" );
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document.write( "Next, &nbsp;add the equation &nbsp;(*)&nbsp; and the second equation of the system. &nbsp;You will get\r<BR>\n" );
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document.write( "2y = 0, &nbsp;&nbsp;and, &nbsp;&nbsp;hence, &nbsp;&nbsp;y = 0.\r<BR>\n" );
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document.write( "Finally, &nbsp;add the equation &nbsp;(*)&nbsp; and the third equation of the system. &nbsp;You will get\r<BR>\n" );
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document.write( "2z = 0, &nbsp;&nbsp;and, &nbsp;&nbsp;hence, &nbsp;&nbsp;z = 0.\r<BR>\n" );
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document.write( "Thus your system has a unique solution &nbsp;&nbsp;x = y = z = 0.\r<BR>\n" );
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document.write( "Hence, &nbsp;the expression under the question is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%28x%2B1%29%29 ALIGN=MIDDLE  ALT=\"%281%2F%28x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%28y%2B1%29%29 ALIGN=MIDDLE  ALT=\"%281%2F%28y%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%28z%2B1%29%29 ALIGN=MIDDLE  ALT=\"%281%2F%28z%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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