document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=71396>Question 71396</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Combine: (3/x(to the 2nd) + 3x - 4) - (4/x(to the 2nd) - 6x - 40)\r<BR>\n" );
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document.write( "Please show work and solution </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #51072 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=51072\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Combine <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2Fx%5E2+%2B+3x+-+4%29+-+%284%2Fx%5E2+-+6x+-+40%29 ALIGN=MIDDLE  ALT=\"%283%2Fx%5E2+%2B+3x+-+4%29+-+%284%2Fx%5E2+-+6x+-+40%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "One of the first thing you can do is remove the parentheses by using the rules:<BR>\n" );
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document.write( "(1) If a set of parentheses is preceded by a plus sign (no sign at all is assumed to be plus),<BR>\n" );
document.write( "then just remove the parentheses without making changes to the terms within the parentheses.<BR>\n" );
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document.write( "(2) If a set of parentheses is preceded by a minus sign you can remove the parentheses,<BR>\n" );
document.write( "but you must change the signs of the terms within the parentheses. (A term that was plus<BR>\n" );
document.write( "when it was within the parentheses becomes minus when the parentheses are removed. And a term<BR>\n" );
document.write( "that was minus when it was within the parentheses becomes plus when the parentheses <BR>\n" );
document.write( "are removed.)<BR>\n" );
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document.write( "Note that the first set of parentheses (reading from left to right) does not have a <BR>\n" );
document.write( "sign preceding it.  Therefore, it is presumed to have a preceding plus sign and you can <BR>\n" );
document.write( "remove the parentheses with out changing terms.  This makes the problem:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Fx%5E2+%2B+3x+-+4+-+%284%2Fx%5E2+-+6x+-+40%29 ALIGN=MIDDLE  ALT=\"3%2Fx%5E2+%2B+3x+-+4+-+%284%2Fx%5E2+-+6x+-+40%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The remaining set of parentheses is preceded by a minus sign.  Therefore, when you remove<BR>\n" );
document.write( "the parentheses you must also change the sign of the three terms inside.  When you do<BR>\n" );
document.write( "this the problem becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Fx%5E2+%2B+3x+-+4+-+4%2Fx%5E2+%2B+6x+%2B+40%29 ALIGN=MIDDLE  ALT=\"3%2Fx%5E2+%2B+3x+-+4+-+4%2Fx%5E2+%2B+6x+%2B+40%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that the +3x and the +6x can be added to give +9x.  Notice also that the -4 and<BR>\n" );
document.write( "the +40 can be added to get + 36.  Make these two substitutions to make the problem<BR>\n" );
document.write( "become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Fx%5E2+-+4%2Fx%5E2+%2B+9x+%2B+36%29 ALIGN=MIDDLE  ALT=\"3%2Fx%5E2+-+4%2Fx%5E2+%2B+9x+%2B+36%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now notice that you have two fractions left to deal with.  They both have the same<BR>\n" );
document.write( "denominator so their numerators can be added and the resulting term put over the common <BR>\n" );
document.write( "denominator.  Their numerators are +3 and -4.  When you add them the answer is -1 and<BR>\n" );
document.write( "this is put over the common denominator to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2Fx%5E2 ALIGN=MIDDLE  ALT=\"-1%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  When you substitute <BR>\n" );
document.write( "this into the equation, the result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2Fx%5E2+%2B+9x+%2B+36%29 ALIGN=MIDDLE  ALT=\"-1%2Fx%5E2+%2B+9x+%2B+36%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "As far as I'm concerned, that answer is correct.  However, maybe your teacher wants <BR>\n" );
document.write( "everything over the common denominator of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  If so, multiply the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x ALIGN=MIDDLE  ALT=\"9x\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Fx%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E3%2Fx%5E2 ALIGN=MIDDLE  ALT=\"9x%5E3%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and then multiply the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36 ALIGN=MIDDLE  ALT=\"36\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Fx%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%2Ax%5E2%2Fx%5E2 ALIGN=MIDDLE  ALT=\"36%2Ax%5E2%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Now all the terms have the common denominator of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so you can add their numerators and get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1+%2B+9x%5E3+%2B+36x%5E2%29%2Fx%5E2 ALIGN=MIDDLE  ALT=\"%28-1+%2B+9x%5E3+%2B+36x%5E2%29%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and as a<BR>\n" );
document.write( "final <BR>\n" );
document.write( "touch you can arrange the numerator in descending powers of x so that the answer is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289x%5E3+%2B+36x%5E2+-1%29%2Fx%5E2 ALIGN=MIDDLE  ALT=\"%289x%5E3+%2B+36x%5E2+-1%29%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Check all the math above.  It's pretty early in the morning and I haven't had a chance to<BR>\n" );
document.write( "become fully awake. Feel free to correct any careless mistakes you find. I hope this <BR>\n" );
document.write( "problem helps you to become familiar with some of the ways you can simplify algebraic<BR>\n" );
document.write( "expressions. </SPAN>\n" );
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