document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=135041>Question 135041</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify completely:\r<BR>\n" );
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document.write( "y over x - x over y divided by 2 over y -2 over x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #99049 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=99049\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y over x - x over y divided by 2 over y -2 over x<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2Fx+-+x%2Fy ALIGN=MIDDLE  ALT=\"y%2Fx+-+x%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Fy+-+2%2Fx ALIGN=MIDDLE  ALT=\"2%2Fy+-+2%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Place them over a common denominator<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y%2Ay+-+x%2Ax%29%29%2F%28xy%29 ALIGN=MIDDLE  ALT=\"%28%28y%2Ay+-+x%2Ax%29%29%2F%28xy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282x+-+2y%29%29%2F%28xy%29 ALIGN=MIDDLE  ALT=\"%28%282x+-+2y%29%29%2F%28xy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y%5E2+-+x%5E2%29%29%2F%28xy%29 ALIGN=MIDDLE  ALT=\"%28%28y%5E2+-+x%5E2%29%29%2F%28xy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282x+-+2y%29%29%2F%28xy%29 ALIGN=MIDDLE  ALT=\"%28%282x+-+2y%29%29%2F%28xy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Invert the dividing fraction and multiply:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y%5E2+-+x%5E2%29%29%2F%28xy%29 ALIGN=MIDDLE  ALT=\"%28%28y%5E2+-+x%5E2%29%29%2F%28xy%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28xy%29%2F%28%282x-2y%29%29 ALIGN=MIDDLE  ALT=\"%28xy%29%2F%28%282x-2y%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cancel the xy's and you have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y%5E2+-+x%5E2%29%29%2F%28%282x-2y%29%29 ALIGN=MIDDLE  ALT=\"%28%28y%5E2+-+x%5E2%29%29%2F%28%282x-2y%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y%5E2+-+x%5E2%29%29%2F%282%28x-y%29%29 ALIGN=MIDDLE  ALT=\"%28%28y%5E2+-+x%5E2%29%29%2F%282%28x-y%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "I failed to notice that y^2 - x^2 is the difference squares & can be factored to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y-x%29%28y%2Bx%29%29%2F%282%28x-y%29%29 ALIGN=MIDDLE  ALT=\"%28%28y-x%29%28y%2Bx%29%29%2F%282%28x-y%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cancel (y-x) leaving us with:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%29%2F2 ALIGN=MIDDLE  ALT=\"%28x%2By%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "I can't believe that I keep screwing this up:<BR>\n" );
document.write( "In order cancel y-x we have to change the sign in the denominator. Make it a -2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y-x%29%28y%2Bx%29%29%2F%28-2%28y-x%29%29 ALIGN=MIDDLE  ALT=\"%28%28y-x%29%28y%2Bx%29%29%2F%28-2%28y-x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cancel (y-x) leaving us with:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%29%2F%28-2%29 ALIGN=MIDDLE  ALT=\"%28x%2By%29%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28%28x%2By%29%29%2F2 ALIGN=MIDDLE  ALT=\"-%28%28x%2By%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Sorry if I got you thoroughly confused. Do you have any questions? </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );