document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1006591>Question 1006591</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Regarding equations with fractions:\r<BR>\n" );
document.write( "\n" );
document.write( "Which of the following is equivalent to 1/x-2 divided by 1/x+2?\r<BR>\n" );
document.write( "\n" );
document.write( "Algebraically, I flip the denominator and multiply the terms to get x+2/x-2.\r<BR>\n" );
document.write( "\n" );
document.write( "But, of course, that's not an answer choice.\r<BR>\n" );
document.write( "\n" );
document.write( "The correct answer choice is supposedly 1 + (4/x-2)! \r<BR>\n" );
document.write( "\n" );
document.write( "How do I get there?\r<BR>\n" );
document.write( "\n" );
document.write( "Would appreciate any help.\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #622715 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=622715\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Honestly, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a perfectly valid answer. If I were grading your homework, then I would accept that answer.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Here's what they did to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B4%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"1%2B4%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%2B2-2%29%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%2B2-2%29%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Notice the +2-2 up top. This is equal to 0. Adding 0 doesn't change 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=%28x-2%2B2%2B2%29%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"%28x-2%2B2%2B2%29%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > move the -2 next to the x to get \"x-2\"\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-2%29%2B%282%2B2%29%29%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"%28%28x-2%29%2B%282%2B2%29%29%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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-2%29%2B%284%29%29%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"%28%28x-2%29%2B%284%29%29%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%2F%28x-2%29%2B4%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"%28x-2%29%2F%28x-2%29%2B4%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction using the rule <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%2Fc+=+a%2Fc+%2B+b%2Fc ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%2Fc+=+a%2Fc+%2B+b%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B4%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"1%2B4%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the rule <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fx+=+1 ALIGN=MIDDLE  ALT=\"x%2Fx+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (x is nonzero)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So that shows how <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B4%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"1%2B4%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Side Note: you can also use polynomial long division or synthetic division to find that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%2F%28x-2%29=1%2B4%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%2F%28x-2%29=1%2B4%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );