document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=122901>Question 122901</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you help me simplify this expression, using only positive exponents in the answer...I don't quite understand these, so if you could be detailed, I would appriciate it.\r<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 #90213 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=90213\">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=%28x%5E-1-y%5E-1%29%2F%28x%5E-2-y%5E-2%29 ALIGN=MIDDLE  ALT=\"%28x%5E-1-y%5E-1%29%2F%28x%5E-2-y%5E-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with given expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Fx-1%2Fy%29%2F%281%2Fx%5E2-1%2Fy%5E2%29 ALIGN=MIDDLE  ALT=\"%281%2Fx-1%2Fy%29%2F%281%2Fx%5E2-1%2Fy%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Flip the bases that have negative exponents. Remember <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E-1=1%2Fx%5E1=1%2Fx ALIGN=MIDDLE  ALT=\"x%5E-1=1%2Fx%5E1=1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E-2=1%2Fx%5E2 ALIGN=MIDDLE  ALT=\"x%5E-2=1%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y%2Fy%29%281%2Fx%29-%28x%2Fx%29%281%2Fy%29%29%2F%281%2Fx%5E2-1%2Fy%5E2%29 ALIGN=MIDDLE  ALT=\"%28%28y%2Fy%29%281%2Fx%29-%28x%2Fx%29%281%2Fy%29%29%2F%281%2Fx%5E2-1%2Fy%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the first fraction <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx ALIGN=MIDDLE  ALT=\"1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > 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;\" >. Multiply the second fraction <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fy ALIGN=MIDDLE  ALT=\"1%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" > 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" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2Fxy-x%2Fxy%29%2F%281%2Fx%5E2-1%2Fy%5E2%29 ALIGN=MIDDLE  ALT=\"%28y%2Fxy-x%2Fxy%29%2F%281%2Fx%5E2-1%2Fy%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the fractions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y-x%29%2F%28xy%29%29%2F%281%2Fx%5E2-1%2Fy%5E2%29 ALIGN=MIDDLE  ALT=\"%28%28y-x%29%2F%28xy%29%29%2F%281%2Fx%5E2-1%2Fy%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions in the numerator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y-x%29%2F%28xy%29%29%2F%28%28y%5E2%2Fy%5E2%29%281%2Fx%5E2%29-%28x%5E2%2Fx%5E2%29%281%2Fy%5E2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the first fraction <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx%5E2 ALIGN=MIDDLE  ALT=\"1%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2Fy%5E2 ALIGN=MIDDLE  ALT=\"y%5E2%2Fy%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Multiply the second fraction <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fy%5E2 ALIGN=MIDDLE  ALT=\"1%2Fy%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Fx%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y-x%29%2F%28xy%29%29%2F%28%28y%5E2%29%2F%28x%5E2y%5E2%29-%28x%5E2%29%2F%28x%5E2y%5E2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the fractions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y-x%29%2F%28xy%29%29%2F%28%28y%5E2-x%5E2%29%2F%28x%5E2y%5E2%29%29 ALIGN=MIDDLE  ALT=\"%28%28y-x%29%2F%28xy%29%29%2F%28%28y%5E2-x%5E2%29%2F%28x%5E2y%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions in the denominator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y-x%29%2F%28xy%29%29%2A%28%28x%5E2y%5E2%29%2F%28y%5E2-x%5E2%29%29 ALIGN=MIDDLE  ALT=\"%28%28y-x%29%2F%28xy%29%29%2A%28%28x%5E2y%5E2%29%2F%28y%5E2-x%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the first fraction by the reciprocal of the second fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y-x%29%2F%28xy%29%29%2A%28%28x%2Ax%2Ay%2Ay%29%2F%28%28y-x%29%28y%2Bx%29%29%29 ALIGN=MIDDLE  ALT=\"%28%28y-x%29%2F%28xy%29%29%2A%28%28x%2Ax%2Ay%2Ay%29%2F%28%28y-x%29%28y%2Bx%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2y%5E2 ALIGN=MIDDLE  ALT=\"x%5E2y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Ax%2Ay%2Ay ALIGN=MIDDLE  ALT=\"x%2Ax%2Ay%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-x%5E2 ALIGN=MIDDLE  ALT=\"y%5E2-x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (by using the difference of squares formula) to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-x%29%28y%2Bx%29 ALIGN=MIDDLE  ALT=\"%28y-x%29%28y%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%28%28y-x%29%29%2F%28cross%28xy%29%29%29%2A%28%28cross%28x%29%2Ax%2Across%28y%29%2Ay%29%2F%28cross%28%28y-x%29%29%28y%2Bx%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy%2F%28y%2Bx%29 ALIGN=MIDDLE  ALT=\"xy%2F%28y%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E-1-y%5E-1%29%2F%28x%5E-2-y%5E-2%29 ALIGN=MIDDLE  ALT=\"%28x%5E-1-y%5E-1%29%2F%28x%5E-2-y%5E-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy%2F%28y%2Bx%29 ALIGN=MIDDLE  ALT=\"xy%2F%28y%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E-1-y%5E-1%29%2F%28x%5E-2-y%5E-2%29=xy%2F%28y%2Bx%29 ALIGN=MIDDLE  ALT=\"%28x%5E-1-y%5E-1%29%2F%28x%5E-2-y%5E-2%29=xy%2F%28y%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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