document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1023232>Question 1023232</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (3m / 2m^2 + 7m - 15) + (6 / 2m^2 - 3m) + (2m + 3 / 2m^2 + 17m + 35) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #638989 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=638989\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I suspect what you meant is<BR>\n" );
document.write( "3m /(2m^2 + 7m - 15) + 6 /(2m^2 - 3m) + (2m + 3) / (2m^2 + 17m + 35) =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3m+%2F%282m%5E2+%2B+7m+-+15%29+%2B+6+%2F%282m%5E2+-+3m%29+%2B+%282m+%2B+3%29+%2F+%282m%5E2+%2B+17m+%2B+35%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3m%2F%282m%5E2+%2B+7m+-+15%29+%2B+6+%2F%282m%5E2+-+3m%29+%2B+%282m+%2B+3%29+%2F+%282m%5E2+%2B+17m+%2B+35%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3m+%2F%28%28m%2B5%29%282m-3%29%29+%2B+6+%2F%28m%282m-3%29%29+%2B+%282m+%2B+3%29+%2F+%28%282m%2B7%29%28m+%2B+5%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3m%2Am%2A%282m%2B7%29%2F%28m%282m-3%29%282m%2B7%29%28m+%2B+5%29%29+%2B+6%2A%282m%2B7%29%2A%28m+%2B+5%29%2F%28m%282m-3%29%282m%2B7%29%28m+%2B+5%29%29+%2B+%282m+%2B+3%29%2Am%2A%282m-3%29%2F%28m%282m-3%29%282m%2B7%29%28m+%2B+5%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286m%5E3%2B21m%5E2%29%2F%28m%282m-3%29%282m%2B7%29%28m+%2B+5%29%29+%2B+6%2A%282m%5E2+%2B+17m+%2B+35%29%2F%28m%282m-3%29%282m%2B7%29%28m+%2B+5%29%29+%2Bm%2A%284m%5E2-9%29%2F%28m%282m-3%29%282m%2B7%29%28m+%2B+5%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286m%5E3%2B21m%5E2%29%2F%28m%282m-3%29%282m%2B7%29%28m+%2B+5%29%29+%2B+%2812m%5E2+%2B+102m+%2B+210%29%2F%28m%282m-3%29%282m%2B7%29%28m+%2B+5%29%29+%2B%284m%5E3-9m%29%2F%28m%282m-3%29%282m%2B7%29%28m+%2B+5%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810m%5E3%2B33m%5E2%2B93m%2B210%29%2F%28m%282m-3%29%282m%2B7%29%28m+%2B+5%29%29 ALIGN=MIDDLE  ALT=\"%2810m%5E3%2B33m%5E2%2B93m%2B210%29%2F%28m%282m-3%29%282m%2B7%29%28m+%2B+5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "NOTE:<BR>\n" );
document.write( "In the expression 3m/(2m^2 + 7m - 15)  +  6/(2m^2 - 3m)  +  (2m + 3)/(2m^2 + 17m + 35) ,<BR>\n" );
document.write( "the very necessary brackets mean that what what is inside them must be calculated first.<BR>\n" );
document.write( "So in evaluating that expression for any value of m,<BR>\n" );
document.write( "the denominators, and the \"2m + 3\" numerator are calculated first.<BR>\n" );
document.write( "(What would be done next is the three divisions,<BR>\n" );
document.write( "and finally you would add the three calculated quotient values).<BR>\n" );
document.write( "In the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3m+%2F%282m%5E2+%2B+7m+-+15%29+%2B+6+%2F%282m%5E2+-+3m%29+%2B+%282m+%2B+3%29+%2F+%282m%5E2+%2B+17m+%2B+35%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "those long horizontal lines mean that what is below them (and what is above them) must be calculated first.<BR>\n" );
document.write( "Those long horizontal lines have invisible brackets attached,<BR>\n" );
document.write( "but when you cannot type those lines, you must put brackets in the right places.<BR>\n" );
document.write( "If you put brackets in the wrong places, or leave them out,<BR>\n" );
document.write( "you will be misunderstood by computers, most calculators,<BR>\n" );
document.write( "and people who the centuries old \"grammar rules\" of written algebraic expressions.<BR>\n" );
document.write( "because<BR>\n" );
document.write( "(3m / 2m^2 + 7m - 15) + (6 / 2m^2 - 3m) + (2m + 3 / 2m^2 + 17m + 35) =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3m+%2F%282m%5E2%29 ALIGN=MIDDLE  ALT=\"3m+%2F%282m%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%2B%22 ALIGN=MIDDLE  ALT=\"%22%2B%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7m+-+15 ALIGN=MIDDLE  ALT=\"7m+-+15\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%2B%22 ALIGN=MIDDLE  ALT=\"%22%2B%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F%282m%5E2%29 ALIGN=MIDDLE  ALT=\"6%2F%282m%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22-%22 ALIGN=MIDDLE  ALT=\"%22-%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3m+%2B+2m ALIGN=MIDDLE  ALT=\"3m+%2B+2m\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%2B%22 ALIGN=MIDDLE  ALT=\"%22%2B%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%2F%282m%5E2%29 ALIGN=MIDDLE  ALT=\"3+%2F%282m%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%2B%22 ALIGN=MIDDLE  ALT=\"%22%2B%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17m+%2B+35 ALIGN=MIDDLE  ALT=\"17m+%2B+35\"   DISABLED_style= \"max-width:90%; height:auto;\" >= 3m/2m^2 + 7m - 15 + 6/2m^2 - 3m + 2m + 3/2m^2 + 17m + 35 .<BR>\n" );
document.write( "If you want to calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8100%2F%28100-19%29 ALIGN=MIDDLE  ALT=\"8100%2F%28100-19%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=8100/(100-19) ,<BR>\n" );
document.write( "and get the correct answer, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8100%2F%28100-19%29=8100%2F81=100 ALIGN=MIDDLE  ALT=\"8100%2F%28100-19%29=8100%2F81=100\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "you must enter \"8100 / ( 100 - 19 )\" on your calculator or computer.<BR>\n" );
document.write( "If you enter it as \"8100 / 100 - 19 =\" into a calculator,<BR>\n" );
document.write( "or enter \"= 8100 / 100 - 19\" in a spreadsheet in your computer,<BR>\n" );
document.write( "you will get what you asked:<BR>\n" );
document.write( "8100 / 100- 19 =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8100%2F100-19=81-19=62 ALIGN=MIDDLE  ALT=\"8100%2F100-19=81-19=62\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );