document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=191829>Question 191829</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780132356794/algebrahomeworkh>Introductory Algebra for College Students</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Simplify the complex rational expression\r<BR>\n" );
document.write( "\n" );
document.write( "3 + 12/x<BR>\n" );
document.write( "_________\r<BR>\n" );
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document.write( "1 - 16/x^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #143941 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=143941\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Simplify the complex rational expression <BR>\n" );
document.write( "3 + 12/x<BR>\n" );
document.write( "_________ <BR>\n" );
document.write( "1 - 16/x^2<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "= (3x+12)/x // ((x^2-16)/x^2<BR>\n" );
document.write( "The quickest and least error-prone way to do these it make a new fraction by multiplying the \"outside\" terms, in this case (3x+12) and x^2 (NUM) and the \"inside\" terms, x*(x^2-16).<BR>\n" );
document.write( "--> x^2*(3x+12)/(x*(x^2-16))<BR>\n" );
document.write( "= x*3*(x+4)/(x+4)*(x-4)<BR>\n" );
document.write( "= 3x/(x-4)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );