document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=188737>Question 188737</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this problem. I am confused and am trying to learn how to solve this type of problem. It is a fraction on top of a fraction and needs to be simplified; If anyone can help me understand this I would greatly appreciate it. Thank you.\r<BR>\n" );
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document.write( " 2<BR>\n" );
document.write( "---  +1<BR>\n" );
document.write( "x+3<BR>\n" );
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document.write( "4<BR>\n" );
document.write( "---- +2<BR>\n" );
document.write( "x+3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #141553 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=141553\">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=%282%2F%28x%2B3%29%2B1%29%2F%284%2F%28x%2B3%29%2B2%29 ALIGN=MIDDLE  ALT=\"%282%2F%28x%2B3%29%2B1%29%2F%284%2F%28x%2B3%29%2B2%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=%282%2F%28x%2B3%29%2B%28x%2B3%29%2F%28x%2B3%29%29%2F%284%2F%28x%2B3%29%2B2%29 ALIGN=MIDDLE  ALT=\"%282%2F%28x%2B3%29%2B%28x%2B3%29%2F%28x%2B3%29%29%2F%284%2F%28x%2B3%29%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the term \"1\" in the numerator by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%2F%28x%2B3%29 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%2F%28x%2B3%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=%28%282%2Bx%2B3%29%2F%28x%2B3%29%29%2F%284%2F%28x%2B3%29%2B2%29 ALIGN=MIDDLE  ALT=\"%28%282%2Bx%2B3%29%2F%28x%2B3%29%29%2F%284%2F%28x%2B3%29%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the upper fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B5%29%2F%28x%2B3%29%29%2F%284%2F%28x%2B3%29%2B2%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B5%29%2F%28x%2B3%29%29%2F%284%2F%28x%2B3%29%2B2%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=%28%28x%2B5%29%2F%28x%2B3%29%29%2F%284%2F%28x%2B3%29%2B%282%28x%2B3%29%29%2F%28x%2B3%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B5%29%2F%28x%2B3%29%29%2F%284%2F%28x%2B3%29%2B%282%28x%2B3%29%29%2F%28x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the term \"2\" in the denominator by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%2F%28x%2B3%29 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%2F%28x%2B3%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=%28%28x%2B5%29%2F%28x%2B3%29%29%2F%284%2F%28x%2B3%29%2B%282x%2B6%29%2F%28x%2B3%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B5%29%2F%28x%2B3%29%29%2F%284%2F%28x%2B3%29%2B%282x%2B6%29%2F%28x%2B3%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=%28%28x%2B5%29%2F%28x%2B3%29%29%2F%28%284%2B2x%2B6%29%2F%28x%2B3%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B5%29%2F%28x%2B3%29%29%2F%28%284%2B2x%2B6%29%2F%28x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the lower fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B5%29%2F%28x%2B3%29%29%2F%28%282x%2B10%29%2F%28x%2B3%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B5%29%2F%28x%2B3%29%29%2F%28%282x%2B10%29%2F%28x%2B3%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=%28%28x%2B5%29%2F%28x%2B3%29%29%2A%28%28x%2B3%29%2F%282x%2B10%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B5%29%2F%28x%2B3%29%29%2A%28%28x%2B3%29%2F%282x%2B10%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the upper fraction by the reciprocal of the lower fraction.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B5%29%2F%28x%2B3%29%29%2A%28%28x%2B3%29%2F%282%28x%2B5%29%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B5%29%2F%28x%2B3%29%29%2A%28%28x%2B3%29%2F%282%28x%2B5%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B10 ALIGN=MIDDLE  ALT=\"2x%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%2B5%29 ALIGN=MIDDLE  ALT=\"2%28x%2B5%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=%28%28x%2B5%29%28x%2B3%29%29%2F%282%28x%2B3%29%28x%2B5%29%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B5%29%28x%2B3%29%29%2F%282%28x%2B3%29%28x%2B5%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=%28highlight%28%28x%2B5%29%29highlight%28%28x%2B3%29%29%29%2F%282%2Ahighlight%28%28x%2B3%29%29highlight%28%28x%2B5%29%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Highlight the common terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%28%28x%2B5%29%29cross%28%28x%2B3%29%29%29%2F%282%2Across%28%28x%2B3%29%29cross%28%28x%2B5%29%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel out the common terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F%28x%2B3%29%2B1%29%2F%284%2F%28x%2B3%29%2B2%29 ALIGN=MIDDLE  ALT=\"%282%2F%28x%2B3%29%2B1%29%2F%284%2F%28x%2B3%29%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In other words,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F%28x%2B3%29%2B1%29%2F%284%2F%28x%2B3%29%2B2%29=1%2F2 ALIGN=MIDDLE  ALT=\"%282%2F%28x%2B3%29%2B1%29%2F%284%2F%28x%2B3%29%2B2%29=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E-5 ALIGN=MIDDLE  ALT=\"x%3C%3E-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E-3 ALIGN=MIDDLE  ALT=\"x%3C%3E-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note: in this case, the problem can be simplified in another way:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F%28x%2B3%29%2B1%29%2F%284%2F%28x%2B3%29%2B2%29 ALIGN=MIDDLE  ALT=\"%282%2F%28x%2B3%29%2B1%29%2F%284%2F%28x%2B3%29%2B2%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=%282%2F%28x%2B3%29%2B1%29%2F%282%282%2F%28x%2B3%29%2B1%29%29 ALIGN=MIDDLE  ALT=\"%282%2F%28x%2B3%29%2B1%29%2F%282%282%2F%28x%2B3%29%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the denominator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%282%2F%28x%2B3%29%2B1%29%2F%282%2Ahighlight%28%282%2F%28x%2B3%29%2B1%29%29%29 ALIGN=MIDDLE  ALT=\"highlight%282%2F%28x%2B3%29%2B1%29%2F%282%2Ahighlight%28%282%2F%28x%2B3%29%2B1%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Highlight the common terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%282%2F%28x%2B3%29%2B1%29%2F%282%2Across%28%282%2F%28x%2B3%29%2B1%29%29%29 ALIGN=MIDDLE  ALT=\"cross%282%2F%28x%2B3%29%2B1%29%2F%282%2Across%28%282%2F%28x%2B3%29%2B1%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel out the common terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F%28x%2B3%29%2B1%29%2F%284%2F%28x%2B3%29%2B2%29=1%2F2 ALIGN=MIDDLE  ALT=\"%282%2F%28x%2B3%29%2B1%29%2F%284%2F%28x%2B3%29%2B2%29=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E-5 ALIGN=MIDDLE  ALT=\"x%3C%3E-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E-3 ALIGN=MIDDLE  ALT=\"x%3C%3E-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note: this technique does not always apply. </SPAN>\n" );
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