document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=126340>Question 126340</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0074711571/algebrahomeworkh>Mathematics for Technicians</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I am stuck on this problem after I have tried to work it out several different ways, but am unable to get the same answer as the textbook. Your assistance would be greatly appreciated. Thank you.<BR>\n" );
document.write( "The problem is as follows:<BR>\n" );
document.write( "2+X/X^2+X-3/3X.<BR>\n" );
document.write( "This is how I have gone about this.<BR>\n" );
document.write( "2+X/X^2+X-3/3X<BR>\n" );
document.write( "which gives me<BR>\n" );
document.write( "6X+3X^2/3X^3+X^3-3X^2/3X^3<BR>\n" );
document.write( "which gives me<BR>\n" );
document.write( "6X+3X^2+X^3-3X^2/3X^3<BR>\n" );
document.write( "which gives me<BR>\n" );
document.write( "X^3+3X^2-3X^2+6X/3X^3<BR>\n" );
document.write( "which gives me<BR>\n" );
document.write( "X^3+6X/3X^3<BR>\n" );
document.write( "And I simply cannot see how the textbook has come up with the answer of<BR>\n" );
document.write( "X^2+6/3X^2<BR>\n" );
document.write( "Please would you be able to show me with an explanation as to why each step is done. Thank you so very much.<BR>\n" );
document.write( "Cheers D. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #92547 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=92547\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Bx%29%2Fx%5E2%2B%28x-3%29%2F3x ALIGN=MIDDLE  ALT=\"%282%2Bx%29%2Fx%5E2%2B%28x-3%29%2F3x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You would have had an easier time of it had you chosen the LOWEST common denominator, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2 ALIGN=MIDDLE  ALT=\"3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > rather than using the simple product of the denominators <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E3 ALIGN=MIDDLE  ALT=\"3x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "However, you have done everything else correctly, except for taking the final step.\r<BR>\n" );
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document.write( "Your answer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E3%2B6x%29%2F3x%5E3 ALIGN=MIDDLE  ALT=\"%28x%5E3%2B6x%29%2F3x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, can be rewritten by factoring as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%28x%5E2%2B6%29%29%2F%28x%283x%5E2%29%29 ALIGN=MIDDLE  ALT=\"%28x%28x%5E2%2B6%29%29%2F%28x%283x%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Then divide out the common factor:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%28x%29%28x%5E2%2B6%29%29%2F%28cross%28x%29%283x%5E2%29%29 ALIGN=MIDDLE  ALT=\"%28cross%28x%29%28x%5E2%2B6%29%29%2F%28cross%28x%29%283x%5E2%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=%28x%5E2%2B6%29%2F%283x%5E2%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B6%29%2F%283x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is the answer from the book.  Technically, your answer was correct, it just wasn't reduced to lowest terms.\r<BR>\n" );
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