document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=258179>Question 258179</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify x/x-4 divided by 2+ x/x-4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #190062 by </B><A HREF=/tutors/aboutme.mpl?userid=PRMath><B>PRMath(133)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=PRMath><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=190062\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> FIRST you have to remember some grade school info about dividing fractions.  If you had <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;\" > divided by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4 ALIGN=MIDDLE  ALT=\"3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > you would do this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29+%2A+%284%2F3%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29+%2A+%284%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "See how the 2nd fraction was \"flipped\" and the problem became a multiplication problem?   Thennnn you would just multiply the numerator times the numerator and the denominator times the denominator.  Let's see that:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2+%2A+4%2F3+=+4%2F6 ALIGN=MIDDLE  ALT=\"1%2F2+%2A+4%2F3+=+4%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F6 ALIGN=MIDDLE  ALT=\"4%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be reduced by dividing the numerator and denominator by 2, which is:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Ok, so your problem is this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29%2F%28x-4%29 ALIGN=MIDDLE  ALT=\"%28x%29%2F%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > divided by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2B+x%29%2F%28x-4%29 ALIGN=MIDDLE  ALT=\"%282%2B+x%29%2F%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Flip the 2nd fraction and then multiply until you have this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29%2F%28x-4%29 ALIGN=MIDDLE  ALT=\"%28x%29%2F%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%2F%282%2Bx%29 ALIGN=MIDDLE  ALT=\"%28x-4%29%2F%282%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now the problem is multiplication and since you are multiplying you can cancel some things out.\r<BR>\n" );
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document.write( "The (x - 4) in the numerator will cancel the (x - 4) in the denominator.   You are then left with:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29%2F%282+%2B+x%29 ALIGN=MIDDLE  ALT=\"%28x%29%2F%282+%2B+x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If you go to YouTube and do a search for PRMathChicago, you'll find other problems like these.  You can watch the videos similar to this problem, and get some extra practice if you'd like.\r<BR>\n" );
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document.write( "I hope this helps. :-) </SPAN>\n" );
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