document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=172899>Question 172899</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977258/algebrahomeworkh>Algebra and Trigonometry Structure and Method book 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I have been struggling to figure out this math problem and I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!!\r<BR>\n" );
document.write( "\n" );
document.write( "Complex fractions<BR>\n" );
document.write( "(x+y/x-y) over (1/x)-(1/y) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #127750 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=127750\">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=%28%28x%2By%29%2F%28x-y%29%29%2F%281%2Fx-1%2Fy%29 ALIGN=MIDDLE  ALT=\"%28%28x%2By%29%2F%28x-y%29%29%2F%281%2Fx-1%2Fy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's focus on the denominator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx-1%2Fy ALIGN=MIDDLE  ALT=\"1%2Fx-1%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" > for now\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx-1%2Fy ALIGN=MIDDLE  ALT=\"1%2Fx-1%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the denominator \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2F%28xy%29-1%2Fy ALIGN=MIDDLE  ALT=\"y%2F%28xy%29-1%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the first fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2Fy ALIGN=MIDDLE  ALT=\"y%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2F%28xy%29-x%2F%28xy%29 ALIGN=MIDDLE  ALT=\"y%2F%28xy%29-x%2F%28xy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the second fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fx ALIGN=MIDDLE  ALT=\"x%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-x%29%2F%28xy%29 ALIGN=MIDDLE  ALT=\"%28y-x%29%2F%28xy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions (this only possible now that the denominators are equal)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the expression \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2By%29%2F%28x-y%29%29%2F%281%2Fx-1%2Fy%29 ALIGN=MIDDLE  ALT=\"%28%28x%2By%29%2F%28x-y%29%29%2F%281%2Fx-1%2Fy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now becomes\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2By%29%2F%28x-y%29%29%2F%28%28y-x%29%2F%28xy%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2By%29%2F%28x-y%29%29%2F%28%28y-x%29%2F%28xy%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2By%29%2F%28x-y%29%29%28%28xy%29%2F%28y-x%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2By%29%2F%28x-y%29%29%28%28xy%29%2F%28y-x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the first fraction <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%29%2F%28x-y%29 ALIGN=MIDDLE  ALT=\"%28x%2By%29%2F%28x-y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > by the reciprocal of the second fraction <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-x%29%2F%28xy%29 ALIGN=MIDDLE  ALT=\"%28y-x%29%2F%28xy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2By%29%2F%28x-y%29%29%28%28xy%29%2F%28-%28x-y%29%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2By%29%2F%28x-y%29%29%28%28xy%29%2F%28-%28x-y%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-x ALIGN=MIDDLE  ALT=\"y-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28x-y%29 ALIGN=MIDDLE  ALT=\"-%28x-y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2By%29%2F%28x-y%29%29%28-%28xy%29%2F%28%28x-y%29%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2By%29%2F%28x-y%29%29%28-%28xy%29%2F%28%28x-y%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28%28x%2By%29%28xy%29%29%2F%28%28x-y%29%28x-y%29%29 ALIGN=MIDDLE  ALT=\"-%28%28x%2By%29%28xy%29%29%2F%28%28x-y%29%28x-y%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28xy%28x%2By%29%29%2F%28%28x-y%29%5E2%29 ALIGN=MIDDLE  ALT=\"-%28xy%28x%2By%29%29%2F%28%28x-y%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2By%29%2F%28x-y%29%29%2F%281%2Fx-1%2Fy%29 ALIGN=MIDDLE  ALT=\"%28%28x%2By%29%2F%28x-y%29%29%2F%281%2Fx-1%2Fy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28xy%28x%2By%29%29%2F%28%28x-y%29%5E2%29 ALIGN=MIDDLE  ALT=\"-%28xy%28x%2By%29%29%2F%28%28x-y%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );