document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=132965>Question 132965</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0201525267/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> 1-i/1+i*2+i/1+i </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #97173 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=97173\">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%281-i%29%2F%281%2Bi%29%29%2A%28%282%2Bi%29%2F%281%2Bi%29%29 ALIGN=MIDDLE  ALT=\"%28%281-i%29%2F%281%2Bi%29%29%2A%28%282%2Bi%29%2F%281%2Bi%29%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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-i%29%282%2Bi%29%2F%281%2Bi%29%281%2Bi%29 ALIGN=MIDDLE  ALT=\"%281-i%29%282%2Bi%29%2F%281%2Bi%29%281%2Bi%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=%282%2Bi-2i-i%5E2%29%2F%281%2Bi%29%281%2Bi%29 ALIGN=MIDDLE  ALT=\"%282%2Bi-2i-i%5E2%29%2F%281%2Bi%29%281%2Bi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Foil the numerator\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=%282-i-i%5E2%29%2F%281%2Bi%29%281%2Bi%29 ALIGN=MIDDLE  ALT=\"%282-i-i%5E2%29%2F%281%2Bi%29%281%2Bi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\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=%282-i-%28-1%29%29%2F%281%2Bi%29%281%2Bi%29 ALIGN=MIDDLE  ALT=\"%282-i-%28-1%29%29%2F%281%2Bi%29%281%2Bi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2 ALIGN=MIDDLE  ALT=\"i%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > with -1\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=%283-i%29%2F%281%2Bi%29%281%2Bi%29 ALIGN=MIDDLE  ALT=\"%283-i%29%2F%281%2Bi%29%281%2Bi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Combine like terms\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=%283-i%29%2F%281%2Bi%2Bi%2Bi%5E2%29 ALIGN=MIDDLE  ALT=\"%283-i%29%2F%281%2Bi%2Bi%2Bi%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Foil 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=%283-i%29%2F%281%2B2i%2Bi%5E2%29 ALIGN=MIDDLE  ALT=\"%283-i%29%2F%281%2B2i%2Bi%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Combine like terms\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=%283-i%29%2F%281%2B2i%2B%28-1%29%29 ALIGN=MIDDLE  ALT=\"%283-i%29%2F%281%2B2i%2B%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2 ALIGN=MIDDLE  ALT=\"i%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > with -1\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=%283-i%29%2F%282i%29 ALIGN=MIDDLE  ALT=\"%283-i%29%2F%282i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Combine like terms\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%283-i%29%2F%282i%29%29%28%282i%29%2F%282i%29%29 ALIGN=MIDDLE  ALT=\"%28%283-i%29%2F%282i%29%29%28%282i%29%2F%282i%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Multiply the fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282i%29%2F%282i%29 ALIGN=MIDDLE  ALT=\"%282i%29%2F%282i%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=%283-i%29%282i%29%2F%282i%29%282i%29 ALIGN=MIDDLE  ALT=\"%283-i%29%282i%29%2F%282i%29%282i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Multiply 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=%283-i%29%282i%29%2F%284i%5E2%29 ALIGN=MIDDLE  ALT=\"%283-i%29%282i%29%2F%284i%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2i ALIGN=MIDDLE  ALT=\"2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2i ALIGN=MIDDLE  ALT=\"2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4i%5E2 ALIGN=MIDDLE  ALT=\"4i%5E2\"   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=%283-i%29%282i%29%2F%284%28-1%29%29 ALIGN=MIDDLE  ALT=\"%283-i%29%282i%29%2F%284%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Replace  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2 ALIGN=MIDDLE  ALT=\"i%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > with -1\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=%283-i%29%282i%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"%283-i%29%282i%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Multiply\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=%286i-2i%5E2%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"%286i-2i%5E2%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Distribute\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=%286i-2%28-1%29%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"%286i-2%28-1%29%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Replace  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2 ALIGN=MIDDLE  ALT=\"i%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > with -1\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=%286i%2B2%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"%286i%2B2%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Multiply\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=%282%2B6i%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"%282%2B6i%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Rearrange the terms\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=%282%29%2F%28-4%29%2B%286i%29%2F%28-4%29 ALIGN=MIDDLE  ALT=\"%282%29%2F%28-4%29%2B%286i%29%2F%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Break up the fraction\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=-1%2F2-%283%2F2%29i ALIGN=MIDDLE  ALT=\"-1%2F2-%283%2F2%29i\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Reduce\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( "\n" );
document.write( "Answer:\r<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%281-i%29%2F%281%2Bi%29%29%2A%28%282%2Bi%29%2F%281%2Bi%29%29 ALIGN=MIDDLE  ALT=\"%28%281-i%29%2F%281%2Bi%29%29%2A%28%282%2Bi%29%2F%281%2Bi%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F2-%283%2F2%29i ALIGN=MIDDLE  ALT=\"-1%2F2-%283%2F2%29i\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281-i%29%2F%281%2Bi%29%29%2A%28%282%2Bi%29%2F%281%2Bi%29%29=-1%2F2-%283%2F2%29i ALIGN=MIDDLE  ALT=\"%28%281-i%29%2F%281%2Bi%29%29%2A%28%282%2Bi%29%2F%281%2Bi%29%29=-1%2F2-%283%2F2%29i\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );