document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117079>Question 117079</A>: <I><SPAN STYLE=\"word-break: break-all;\"> umm, hello??? can anybody help me with my algebra problem??\r<BR>\n" );
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document.write( "the direction is to \"Simplify each of the  following complex rational expressions.\r<BR>\n" );
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document.write( "                      2  -  1/[2+[1 /{(x-1)/x}]\r<BR>\n" );
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document.write( "                            \r<BR>\n" );
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document.write( "I'm very sorry because i don't know how to type it in. But  i hope you could give me your generous help by answering the question.. thnx!! \r<BR>\n" );
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document.write( "                                                  _good luck_<BR>\n" );
document.write( "                                                   _angELz_ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85140 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=85140\">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=2-1%2F%282%2B1%2F%28%28x-1%29%2Fx%29%29 ALIGN=MIDDLE  ALT=\"2-1%2F%282%2B1%2F%28%28x-1%29%2Fx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-1%2F%282%2Bx%2F%28x-1%29%29%29 ALIGN=MIDDLE  ALT=\"2-1%2F%282%2Bx%2F%28x-1%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28%28x-1%29%2Fx%29 ALIGN=MIDDLE  ALT=\"1%2F%28%28x-1%29%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"x%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. What's really happening is I'm taking the reciprocal of this fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-1%2F%28%282%29%28%28x-1%29%2F%28x-1%29%29%2Bx%2F%28x-1%29%29%29 ALIGN=MIDDLE  ALT=\"2-1%2F%28%282%29%28%28x-1%29%2F%28x-1%29%29%2Bx%2F%28x-1%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"%28x-1%29%2F%28x-1%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=2-1%2F%28%282x-2%29%2F%28x-1%29%2Bx%2F%28x-1%29%29%29 ALIGN=MIDDLE  ALT=\"2-1%2F%28%282x-2%29%2F%28x-1%29%2Bx%2F%28x-1%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-1%2F%28%282x-2%2Bx%29%2F%28x-1%29%29%29 ALIGN=MIDDLE  ALT=\"2-1%2F%28%282x-2%2Bx%29%2F%28x-1%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-1%2F%28%283x-2%29%2F%28x-1%29%29%29 ALIGN=MIDDLE  ALT=\"2-1%2F%28%283x-2%29%2F%28x-1%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-%28x-1%29%2F%283x-2%29 ALIGN=MIDDLE  ALT=\"2-%28x-1%29%2F%283x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28%283x-2%29%2F%28x-1%29%29 ALIGN=MIDDLE  ALT=\"1%2F%28%283x-2%29%2F%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%2F%283x-2%29 ALIGN=MIDDLE  ALT=\"%28x-1%29%2F%283x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > by once again taking the reciprocal\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28%283x-2%29%2F%283x-2%29%29-%28x-1%29%2F%283x-2%29 ALIGN=MIDDLE  ALT=\"2%28%283x-2%29%2F%283x-2%29%29-%28x-1%29%2F%283x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x-2%29%2F%283x-2%29 ALIGN=MIDDLE  ALT=\"%283x-2%29%2F%283x-2%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=%286x-4%29%2F%283x-2%29-%28x-1%29%2F%283x-2%29 ALIGN=MIDDLE  ALT=\"%286x-4%29%2F%283x-2%29-%28x-1%29%2F%283x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286x-4-%28x-1%29%29%2F%283x-2%29 ALIGN=MIDDLE  ALT=\"%286x-4-%28x-1%29%29%2F%283x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286x-4-x%2B1%29%2F%283x-2%29 ALIGN=MIDDLE  ALT=\"%286x-4-x%2B1%29%2F%283x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute the negative\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x-3%29%2F%283x-2%29 ALIGN=MIDDLE  ALT=\"%285x-3%29%2F%283x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-1%2F%282%2B1%2F%28%28x-1%29%2Fx%29%29 ALIGN=MIDDLE  ALT=\"2-1%2F%282%2B1%2F%28%28x-1%29%2Fx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x-3%29%2F%283x-2%29 ALIGN=MIDDLE  ALT=\"%285x-3%29%2F%283x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-1%2F%282%2B1%2F%28%28x-1%29%2Fx%29%29=%285x-3%29%2F%283x-2%29 ALIGN=MIDDLE  ALT=\"2-1%2F%282%2B1%2F%28%28x-1%29%2Fx%29%29=%285x-3%29%2F%283x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. You can verify this if you graph the original and the simplified expressions and you'll notice that they overlap. So this visually verifies our answer. </SPAN>\n" );
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