document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=175668>Question 175668</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977258/algebrahomeworkh>Algebra and Trigonometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> u+1/1+1/u<BR>\n" );
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document.write( "1/u+1\r<BR>\n" );
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document.write( "Okay, it sounds likee, u plus 1 over 1 plus 1 over u. alll of that over (divided by) , 1 over u+1\r<BR>\n" );
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document.write( "I can't figure out how to do it.\r<BR>\n" );
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document.write( "Thank youuu. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130777 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=130777\">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=%28%28u+%2B+1%29%2F%281+%2B+%281%2Fu%29%29%29%2F%281%2F%28u+%2B+1%29%29 ALIGN=MIDDLE  ALT=\"%28%28u+%2B+1%29%2F%281+%2B+%281%2Fu%29%29%29%2F%281%2F%28u+%2B+1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Start by inverting the denominator fraction ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28u+%2B+1%29 ALIGN=MIDDLE  ALT=\"1%2F%28u+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ) and multiplying times the numerator fraction.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28u+%2B+1%29%2F%281+%2B+%281%2Fu%29%29%29%28%28u+%2B+1%29%2F1%29+=+%28%28u+%2B+1%29%28u+%2B+1%29%29%2F%281+%2B+%281%2Fu%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now your denominator has addition of an integer to a fraction.  The LCD is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u ALIGN=MIDDLE  ALT=\"u\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%2B+%281%2Fu%29+=+%28u+%2B+1%29%2Fu ALIGN=MIDDLE  ALT=\"1+%2B+%281%2Fu%29+=+%28u+%2B+1%29%2Fu\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Replace the denominator with this new expression:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28u+%2B+1%29%28u+%2B+1%29%29%2F%281+%2B+%281%2Fu%29%29=%28%28u+%2B+1%29%28u+%2B+1%29%29%2F%28%28u%2B1%29%2Fu%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Again, invert and multiply:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%28u+%2B+1%29%28u+%2B+1%29%29%2F1%29%28u%2F%28u%2B1%29%29 ALIGN=MIDDLE  ALT=\"%28%28%28u+%2B+1%29%28u+%2B+1%29%29%2F1%29%28u%2F%28u%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Remove like terms from numerator and denominator:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28cross%28%28u+%2B+1%29%29%28u+%2B+1%29%29%2F1%29%28u%2Fcross%28u%2B1%29%29 ALIGN=MIDDLE  ALT=\"%28%28cross%28%28u+%2B+1%29%29%28u+%2B+1%29%29%2F1%29%28u%2Fcross%28u%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%28u+%2B+1%29 ALIGN=MIDDLE  ALT=\"u%28u+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5E2+%2B+u ALIGN=MIDDLE  ALT=\"u%5E2+%2B+u\"   DISABLED_style= \"max-width:90%; height:auto;\" > if you prefer.\r<BR>\n" );
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document.write( "Check the answer:  You can't absolutely prove the answer this way, but you can get a pretty good idea of whether you did the manipulations correctly.  Pick a number.  Best is a small whole number other than zero or one.  Let's try 2.  If u is 2, then plugging 2 into the original expression should yield 2 X (2 + 1) = 6.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282+%2B+1%29%2F%281+%2B+%281%2F2%29%29%29%2F%281%2F%282+%2B+1%29%29 ALIGN=MIDDLE  ALT=\"%28%282+%2B+1%29%2F%281+%2B+%281%2F2%29%29%29%2F%281%2F%282+%2B+1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  You get to do the arithmetic to see if my solution is correct. </SPAN>\n" );
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