document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1175007>Question 1175007</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Good evening (here):<BR>\n" );
document.write( "If may I'd like to give you a bit of background on myself. I'm a 78 yr. old man, retired medical technologist. I recently got the idea I'd like to learn calculus. I discovered free e books on Amazon. I got the precalculus book and soon figured out that I needed to go back to Algebra. So I got their intermediate algebra book. <BR>\n" );
document.write( "I'm now studying multiplying rational functions. Regarding the problem:<BR>\n" );
document.write( "x^2-x/3x^2+27x-30*x^2-100/x^2-10x. I did all the factoring and multiplying, and canceling and came up with an answer of 3. The book and all my other resources ( Math papa, Microsoft problem solver and this site) say the answer is 1/3. What I would like to know is, what is this procedure called<BR>\n" );
document.write( "for finding this solution, why use it now, and when is it necessary to use it. I can find no information on this solution procedure.<BR>\n" );
document.write( " I can be reached at ledfrn@gmail.com. I thank you in advance for your attention to this matter. Roy Ledford </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #800566 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=800566\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "First, get used to using parentheses where necessary.  The expression as you show it,<br><BR>\n" );
document.write( "x^2-x/3x^2+27x-30*x^2-100/x^2-10x<br><BR>\n" );
document.write( "means this:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x%2F3x%5E2%2B27x-30%2Ax%5E2-100%2Fx%5E2-10x ALIGN=MIDDLE  ALT=\"x%5E2-x%2F3x%5E2%2B27x-30%2Ax%5E2-100%2Fx%5E2-10x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That's clearly not what you meant.<br><BR>\n" );
document.write( "The expression you are working with is<br><BR>\n" );
document.write( "((x^2-x)/(3x^2+27x-30))*((x^2-100)/(x^2-10x))<br><BR>\n" );
document.write( "which means this:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%5E2-x%29%2F%283x%5E2%2B27x-30%29%29%2A%28%28x%5E2-100%29%2F%28x%5E2-10x%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%5E2-x%29%2F%283x%5E2%2B27x-30%29%29%2A%28%28x%5E2-100%29%2F%28x%5E2-10x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Multiplying rational functions is just like multiplying numerical fractions.  If you had, for example,<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815%2F8%29%2A%2816%2F3%29 ALIGN=MIDDLE  ALT=\"%2815%2F8%29%2A%2816%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "you could multiply the numerators and multiply the denominators and simplify the resulting fraction:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815%2F8%29%2A%2816%2F3%29+=+240%2F24+=+10 ALIGN=MIDDLE  ALT=\"%2815%2F8%29%2A%2816%2F3%29+=+240%2F24+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "But it would be easier if you simplified the product before doing any multiplication:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815%2F8%29%2A%2816%2F3%29+=+%2815%2A16%29%2F%288%2A3%29+=+%2815%2F3%29%2816%2F8%29+=+5%2A2+=+10 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "When multiplying rational fractions you DEFINITELY want to factor the expressions and simplify where possible before performing any multiplication.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%5E2-x%29%2F%283x%5E2%2B27x-30%29%29%2A%28%28x%5E2-100%29%2F%28x%5E2-10x%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%5E2-x%29%2F%283x%5E2%2B27x-30%29%29%2A%28%28x%5E2-100%29%2F%28x%5E2-10x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%28x%29%28x-1%29%29%2F%283%28x%2B10%29%28x-1%29%29%29%2A%28%28%28x%2B10%29%28x-10%29%29%2F%28%28x%29%28x-10%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "All the factors cancel except for the 3 in the denominator.<br><BR>\n" );
document.write( "So if you got 3 for the answer, you made a mistake very popular among beginning algebra students.  You saw that the only factor left was \"3\", so that was the answer.  But the 3 that is left is in the denominator.  You don't see it, but there is also a \"1\" left in the numerator, making the answer 1/3 instead of 3.<br><BR>\n" );
document.write( "So it looks as if you did all the factoring and canceling of common factors correctly; you just didn't realize what the final simplified form was.<br><BR>\n" );
document.write( " </SPAN>\n" );
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