document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=186669>Question 186669</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is a problem I need help with.[(1/9)+(1/3x)] / [(x/9)-(1/x)] </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #139931 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=139931\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In order to simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F9%2B1%2F%283x%29%29%2F%28x%2F9-1%2Fx%29 ALIGN=MIDDLE  ALT=\"%281%2F9%2B1%2F%283x%29%29%2F%28x%2F9-1%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > let's simplify the numerator and denominator separately first\r<BR>\n" );
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document.write( "Simplifying the numerator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F9%2B1%2F%283x%29 ALIGN=MIDDLE  ALT=\"1%2F9%2B1%2F%283x%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=1%2F9%2B1%2F%283x%29 ALIGN=MIDDLE  ALT=\"1%2F9%2B1%2F%283x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the numerator. Take note that the LCD <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%2F9x ALIGN=MIDDLE  ALT=\"9x%2F9x\"   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=x%2F%289x%29%2B1%2F%283x%29 ALIGN=MIDDLE  ALT=\"x%2F%289x%29%2B1%2F%283x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the first fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fx ALIGN=MIDDLE  ALT=\"x%2Fx\"   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=x%2F%289x%29%2B3%2F%289x%29 ALIGN=MIDDLE  ALT=\"x%2F%289x%29%2B3%2F%289x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the second fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F3 ALIGN=MIDDLE  ALT=\"3%2F3\"   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=%28x%2B3%29%2F%289x%29 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%2F%289x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add the fractions.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F9%2B1%2F%283x%29=%28x%2B3%29%2F%289x%29 ALIGN=MIDDLE  ALT=\"1%2F9%2B1%2F%283x%29=%28x%2B3%29%2F%289x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E0 ALIGN=MIDDLE  ALT=\"x%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplifying the denominator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F9-1%2Fx ALIGN=MIDDLE  ALT=\"x%2F9-1%2Fx\"   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=x%2F9-1%2Fx ALIGN=MIDDLE  ALT=\"x%2F9-1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the denominator. Take note that the LCD <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%2F9x ALIGN=MIDDLE  ALT=\"9x%2F9x\"   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=%28x%5E2%29%2F%289x%29-1%2Fx ALIGN=MIDDLE  ALT=\"%28x%5E2%29%2F%289x%29-1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the first fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fx ALIGN=MIDDLE  ALT=\"x%2Fx\"   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=%28x%5E2%29%2F%289x%29-9%2F%289x%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%29%2F%289x%29-9%2F%289x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the second fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F9 ALIGN=MIDDLE  ALT=\"9%2F9\"   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=%28x%5E2-9%29%2F%289x%29 ALIGN=MIDDLE  ALT=\"%28x%5E2-9%29%2F%289x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract the fractions.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F9-1%2Fx=%28x%5E2-9%29%2F%289x%29 ALIGN=MIDDLE  ALT=\"x%2F9-1%2Fx=%28x%5E2-9%29%2F%289x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E0 ALIGN=MIDDLE  ALT=\"x%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now that we've simplified the numerator of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F9%2B1%2F%283x%29%29%2F%28x%2F9-1%2Fx%29 ALIGN=MIDDLE  ALT=\"%281%2F9%2B1%2F%283x%29%29%2F%28x%2F9-1%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we then get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B3%29%2F%289x%29%29%2F%28%28x%5E2-9%29%2F%289x%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B3%29%2F%289x%29%29%2F%28%28x%5E2-9%29%2F%289x%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=%28%28x%2B3%29%2F%289x%29%29%2F%28%28x%5E2-9%29%2F%289x%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B3%29%2F%289x%29%29%2F%28%28x%5E2-9%29%2F%289x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the simplified expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B3%29%2F%289x%29%29%2A%28%289x%29%2F%28x%5E2-9%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B3%29%2F%289x%29%29%2A%28%289x%29%2F%28x%5E2-9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the first fraction by the reciprocal of the second fraction.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B3%29%2F%289x%29%29%2A%28%289x%29%2F%28%28x%2B3%29%28x-3%29%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B3%29%2F%289x%29%29%2A%28%289x%29%2F%28%28x%2B3%29%28x-3%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-9 ALIGN=MIDDLE  ALT=\"x%5E2-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%28x-3%29 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%28x-3%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=%289x%28x%2B3%29%29%2F%289x%28x%2B3%29%28x-3%29%29%29 ALIGN=MIDDLE  ALT=\"%289x%28x%2B3%29%29%2F%289x%28x%2B3%29%28x-3%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%289x%29highlight%28%28x%2B3%29%29%29%2F%28highlight%289x%29highlight%28%28x%2B3%29%29%28x-3%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%289x%29cross%28%28x%2B3%29%29%29%2F%28cross%289x%29cross%28%28x%2B3%29%29%28x-3%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%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"1%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\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=%281%2F9%2B1%2F%283x%29%29%2F%28x%2F9-1%2Fx%29 ALIGN=MIDDLE  ALT=\"%281%2F9%2B1%2F%283x%29%29%2F%28x%2F9-1%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplified to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B3%29%2F%289x%29%29%2F%28%28x%5E2-9%29%2F%289x%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B3%29%2F%289x%29%29%2F%28%28x%5E2-9%29%2F%289x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which in turn simplified to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"1%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So in short, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F9%2B1%2F%283x%29%29%2F%28x%2F9-1%2Fx%29 ALIGN=MIDDLE  ALT=\"%281%2F9%2B1%2F%283x%29%29%2F%28x%2F9-1%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"1%2F%28x-3%29\"   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=%281%2F9%2B1%2F%283x%29%29%2F%28x%2F9-1%2Fx%29=1%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"%281%2F9%2B1%2F%283x%29%29%2F%28x%2F9-1%2Fx%29=1%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <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;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E0 ALIGN=MIDDLE  ALT=\"x%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E3 ALIGN=MIDDLE  ALT=\"x%3C%3E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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