document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202559>Question 202559</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the indicated products and quotients.\r<BR>\n" );
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document.write( "1. (9z^3/16xy)(4x/27z^3)\r<BR>\n" );
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document.write( "2. (3m-9/4m+8)(m^2+5m+6/m^2-9)\r<BR>\n" );
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document.write( "3. (y^2+3y-10/3y+15) / (10-5y)\r<BR>\n" );
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document.write( "Thanks\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152779 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=152779\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. (9z^3/16xy)(4x/27z^3) <BR>\n" );
document.write( "2. (3m-9/4m+8)(m^2+5m+6/m^2-9) <BR>\n" );
document.write( "3. (y^2+3y-10/3y+15) / (10-5y) \r<BR>\n" );
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document.write( "Before we do these, we have to agree that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F4+=+1 ALIGN=MIDDLE  ALT=\"4%2F4+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Further, we have to agree that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3%2Fa%5E3+=+1 ALIGN=MIDDLE  ALT=\"a%5E3%2Fa%5E3+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Those are good facts to have in your mind, so let's begin.\r<BR>\n" );
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document.write( "1. (9z^3/16xy)(4x/27z^3)\r<BR>\n" );
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document.write( "I read this as:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9z%5E3%2F16xy ALIGN=MIDDLE  ALT=\"9z%5E3%2F16xy\"   DISABLED_style= \"max-width:90%; height:auto;\" >*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2F27z%5E3 ALIGN=MIDDLE  ALT=\"4x%2F27z%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Because you are multiplying, you can factor terms, just like we did above when we said <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F4=1 ALIGN=MIDDLE  ALT=\"4%2F4=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "SO - let's factor: \r<BR>\n" );
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document.write( "The 9 in the numerator can be factored into the 27 of the denominator to give you <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The 4 in the numerator can be factored into the 16 of the denominator to give you <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E3 ALIGN=MIDDLE  ALT=\"z%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the numerator can be factored into the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E3 ALIGN=MIDDLE  ALT=\"z%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the denominator to give you <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F1 ALIGN=MIDDLE  ALT=\"1%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The \"x\" in the numerator can be factored into the x of the denominator to again give you <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F1 ALIGN=MIDDLE  ALT=\"1%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "What you have left is: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4%283%29y ALIGN=MIDDLE  ALT=\"1%2F4%283%29y\"   DISABLED_style= \"max-width:90%; height:auto;\" >  which is:   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F12y ALIGN=MIDDLE  ALT=\"1%2F12y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2. (3m-9/4m+8)(m^2+5m+6/m^2-9)\r<BR>\n" );
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document.write( "Let's just break this down piece by piece, because it may be quicker:\r<BR>\n" );
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document.write( "Numerator of first fraction:   3m - 9   <BR>\n" );
document.write( "Let's factor out 3:    3(m-3)\r<BR>\n" );
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document.write( "Denominator of first fraction:  4m + 8<BR>\n" );
document.write( "Let's factor out 4:    4(m + 2)\r<BR>\n" );
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document.write( "Numerator of 2nd fraction:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E2%2B5m%2B6 ALIGN=MIDDLE  ALT=\"m%5E2%2B5m%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let's factor this to be:  (m+2)(m+3)\r<BR>\n" );
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document.write( "Denominator:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E2+-9%29 ALIGN=MIDDLE  ALT=\"m%5E2+-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let's factor this to be:  (m+3)(m-3)\r<BR>\n" );
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document.write( "NOW we have: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28m-3%29%28m%2B2%29%28m%2B3%29%2F4%28m%2B2%29%28m%2B3%29%28m-3%29 ALIGN=MIDDLE  ALT=\"3%28m-3%29%28m%2B2%29%28m%2B3%29%2F4%28m%2B2%29%28m%2B3%29%28m-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "NOW factor out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28m-3%29%28m%2B2%29%28m%2B3%29%2F%28m%2B2%29%28m%2B3%29%28m-3%29 ALIGN=MIDDLE  ALT=\"%28m-3%29%28m%2B2%29%28m%2B3%29%2F%28m%2B2%29%28m%2B3%29%28m-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "What you have left is <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;\" >\r<BR>\n" );
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document.write( "3.(y^2+3y-10/3y+15) / (10-5y) \r<BR>\n" );
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document.write( "Numerator of first fraction:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2B3y-10 ALIGN=MIDDLE  ALT=\"y%5E2%2B3y-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factor to:  (y+5)(y-2)\r<BR>\n" );
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document.write( "Denominator of first fraction:3y+15<BR>\n" );
document.write( "Let's factor that to:  3(y+5)\r<BR>\n" );
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document.write( "Second fraction:  10-5y<BR>\n" );
document.write( "Factor to:  5(2-y)\r<BR>\n" );
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document.write( "Now we have:   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B5%29%28y-2%295%282-y%29%2F3%28y%2B5%29 ALIGN=MIDDLE  ALT=\"%28y%2B5%29%28y-2%295%282-y%29%2F3%28y%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(y+5) can factor out of the numerator and denominator so we have left....\r<BR>\n" );
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document.write( "I hope this helps. :-)  </SPAN>\n" );
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