document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=163903>Question 163903</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780073533490/algebrahomeworkh>Elementary and Intermediate</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> 52.) Simplify each complex fraction. Reduce\r<BR>\n" );
document.write( "\n" );
document.write( "1/9+1/3x<BR>\n" );
document.write( "x/9-1/x  this problem has a line between the two which make it one problem.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #120800 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=120800\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "(1/9 + 1/3x)/(x/9-1/x)<BR>\n" );
document.write( "Numerator: (1/9+1/3x); multiply each term by 9x/9x and we get:<BR>\n" );
document.write( "((x+3)/9x)<BR>\n" );
document.write( "Now denominator: (x/9-1/x); multiply each term by 9x/9x and we get<BR>\n" );
document.write( "(x^2-9)/9x but (x^2-9)=(x+3)(x-3) so we have: (x+3)(x-3)/9x\r<BR>\n" );
document.write( "\n" );
document.write( "Next put the numerator and denominator back together and we get:<BR>\n" );
document.write( "((x+3)/9x)/((x+3)(x-3))/9x  Now we can simplify this complex fraction by making the denominator equal to 1.  We can do this by multiplying both the numerator and denominator by 9x/((x+3)(x-3)).  When we do this, we get:<BR>\n" );
document.write( "((x+3)/9x)*(9x/((x+3)(x-3)))/(((x+3)(x-3))/9x)*(9x/((x+3)(x-3))); simplifying, we have:<BR>\n" );
document.write( "1/(x-3)/1 or 1/(x-3)---------------------answer\r<BR>\n" );
document.write( "\n" );
document.write( "Now lets look at the general form of a complex fraction:<BR>\n" );
document.write( "(a/b)/(c/d) Lets make the denominator, (c/d), equal to 1. We can if we multiply the numerator and denominator by (d/c) and we get:\r<BR>\n" );
document.write( "\n" );
document.write( "(a/b)(d/c)/(c/d)(d/c) which equals<BR>\n" );
document.write( "(ad)/(bc)/1=(ad)/(bc)\r<BR>\n" );
document.write( "\n" );
document.write( "After we simplify your problem a little, we can say that:<BR>\n" );
document.write( "a=(x+3)<BR>\n" );
document.write( "b=9x<BR>\n" );
document.write( "c=(x+3)(x-3) and<BR>\n" );
document.write( "d=b=9x<BR>\n" );
document.write( "So the answer is:(ad)/(bc) or (x+3)*9x/(9x*(x+3)(x-3)) cancel like terms<BR>\n" );
document.write( "The 9x's cancel and the (x+3)'s cancel leaving 1/(x-3)<BR>\n" );
document.write( "Hope this helps----ptaylor<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );