document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=74104>Question 74104</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can you help me to explain this equation?\r<BR>\n" );
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document.write( "If f(x)=x-1/x+1 then f(x)+f(1/x)=\r<BR>\n" );
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document.write( "this is a homework assignment..but not in our book..thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #53095 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=53095\">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=f%28x%29=%28x-1%29%2F%28x%2B1%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-1%29%2F%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >If thats what f(x) looks like then we're going to add that to f(1/x). <BR>\n" );
document.write( "To find f(1/x) we simply plug in (1/x) in for every x in the original equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%2Fx%29=%28highlight%281%2Fx%29-1%29%2F%28highlight%281%2Fx%29%2B1%29 ALIGN=MIDDLE  ALT=\"f%281%2Fx%29=%28highlight%281%2Fx%29-1%29%2F%28highlight%281%2Fx%29%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%2Fx%29=%28%281%2Fx%29-%28x%2Fx%29%29%2F%28%281%2Fx%29%2B%28x%2Fx%29%29 ALIGN=MIDDLE  ALT=\"f%281%2Fx%29=%28%281%2Fx%29-%28x%2Fx%29%29%2F%28%281%2Fx%29%2B%28x%2Fx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%2Fx%29=%28%281-x%29%2Fx%29%2F%28%281%2Bx%29%2Fx%29 ALIGN=MIDDLE  ALT=\"f%281%2Fx%29=%28%281-x%29%2Fx%29%2F%28%281%2Bx%29%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%2Fx%29=%28%281-x%29%2Fcross%28x%29%29%2A%28cross%28x%29%2F%281%2Bx%29%29 ALIGN=MIDDLE  ALT=\"f%281%2Fx%29=%28%281-x%29%2Fcross%28x%29%29%2A%28cross%28x%29%2F%281%2Bx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So f(1/x) equals<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%2Fx%29=%28%281-x%29%2F%281%2Bx%29%29 ALIGN=MIDDLE  ALT=\"f%281%2Fx%29=%28%281-x%29%2F%281%2Bx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Add this to f(x)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29%2Bf%281%2Fx%29=%28x-1%29%2F%28x%2B1%29%2B%28%281-x%29%2F%281%2Bx%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29%2Bf%281%2Fx%29=%28x-1%29%2F%28x%2B1%29%2B%28%281-x%29%2F%281%2Bx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29%2Bf%281%2Fx%29=%28x-x%2B1-1%29%2F%28x%2B1%29 ALIGN=MIDDLE  ALT=\"f%28x%29%2Bf%281%2Fx%29=%28x-x%2B1-1%29%2F%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29%2Bf%281%2Fx%29=%280%29%2F%28x%2B1%29 ALIGN=MIDDLE  ALT=\"f%28x%29%2Bf%281%2Fx%29=%280%29%2F%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29%2Bf%281%2Fx%29=0 ALIGN=MIDDLE  ALT=\"f%28x%29%2Bf%281%2Fx%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So for any x <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29%2Bf%281%2Fx%29=0 ALIGN=MIDDLE  ALT=\"f%28x%29%2Bf%281%2Fx%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<p><BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "We can let x equal any number. Lets make x=2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x-1%29%2F%28x%2B1%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-1%29%2F%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >Plug in x=2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%282%29=%282-1%29%2F%282%2B1%29=1%2F3 ALIGN=MIDDLE  ALT=\"f%282%29=%282-1%29%2F%282%2B1%29=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%2Fx%29=%28%281-x%29%2F%281%2Bx%29%29 ALIGN=MIDDLE  ALT=\"f%281%2Fx%29=%28%281-x%29%2F%281%2Bx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >Plug in x=2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%2F2%29=%281-2%29%2F%281%2B2%29 ALIGN=MIDDLE  ALT=\"f%281%2F2%29=%281-2%29%2F%281%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=f%281%2F2%29=-1%2F3 ALIGN=MIDDLE  ALT=\"f%281%2F2%29=-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29%2Bf%281%2Fx%29=f%282%29%2Bf%281%2F2%29=1%2F3-1%2F3=0 ALIGN=MIDDLE  ALT=\"f%28x%29%2Bf%281%2Fx%29=f%282%29%2Bf%281%2F2%29=1%2F3-1%2F3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add the two equations. This shows that our answer works. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );