document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=171512>Question 171512</A>: <I><SPAN STYLE=\"word-break: break-all;\"> simplify the complex fraction 5/6y^2/3/9y^3, 3/x-1/x+3/2/x+5/x+3 How do you do these?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #126757 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=126757\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> OK.  Here's how you do complex fractions:<BR>\n" );
document.write( "Lets look at the complex fraction (a/b)/(c/d).  Now if we can make the denominator (c/d) of this complex fraction equal to 1, then we will have a simple fraction.  We can do this by multiplying both the numerator and denominator by (d/c). When we do this, we get:<BR>\n" );
document.write( "((a/b)*(d/c))/((c/d)*(d/c));  simplifying we have:<BR>\n" );
document.write( "(ad/bc)/1 or ad/bc.\r<BR>\n" );
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document.write( "Now lets apply this to your specific problem:<BR>\n" );
document.write( "(5/6y^2)/(3/9y^3);  multiply numerator and denominator by (9y^3/3):<BR>\n" );
document.write( "((5/6y^2)*(9y^3/3))/((3/9y^3)(9y^3/3)) and we get<BR>\n" );
document.write( "(45y^3)/(18y^2)/1 cancel and simplify and we have:<BR>\n" );
document.write( "5y/2\r<BR>\n" );
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document.write( "For the second part. It is sometimes good to use parens to better clarify the problem:<BR>\n" );
document.write( "3/x-1/x+3/2/x+5/x+3=<BR>\n" );
document.write( "(3/(x-1)/(x-3))/(2/(x+5)/(x+3))<BR>\n" );
document.write( "Now here we have both the numerator and denominator as complex fractions:<BR>\n" );
document.write( "We'll do the numerator first:<BR>\n" );
document.write( "(3/(x-1)/(x-3))=<BR>\n" );
document.write( "(3*(x-3)/(x-1))/((x-1)/(x-3))*(x-3)/(x-1))=<BR>\n" );
document.write( "3(x-3)/(x-1)/1=3(x-3)/(x-1)<BR>\n" );
document.write( "Now the denominator:<BR>\n" );
document.write( "(2/(x+5)/(x+3))=<BR>\n" );
document.write( "(2*(x+3)/(x+5))/((x+5)/(x+3)*(x+3)/(x+5))=<BR>\n" );
document.write( "2(x+3)/(x+5)\r<BR>\n" );
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document.write( "Now we put the numerator and denominator back together and we still have a complex fraction:<BR>\n" );
document.write( "(3(x-3)/(x-1))/(2(x+3)/(x+5))=<BR>\n" );
document.write( "(3(x-3)/(x-1))*(x+5)/2(x+3))/(2(x+3)/(x+5))*(x+5)/2(x+3))=<BR>\n" );
document.write( "(3(x-3)(x+5))/(2(x+3)(x-1))\r<BR>\n" );
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document.write( "Actually, using the little formula that we worked out initially:<BR>\n" );
document.write( "(a/b)/(c/d)=ad/bc, you can determine the a, b , c & d of your problem and simply plug the values in.  For example, look at the numerator that we worked out above:<BR>\n" );
document.write( "(3/(x-1)/(x-3));<BR>\n" );
document.write( "a=3<BR>\n" );
document.write( "b=1<BR>\n" );
document.write( "c=(x-1)<BR>\n" );
document.write( "d=(x-3)<BR>\n" );
document.write( "now pluggin in (ad/bc), we have<BR>\n" );
document.write( "3(x-3)/1(x-1) which is what we got before.\r<BR>\n" );
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document.write( "Hope this helps---ptaylor\r<BR>\n" );
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