document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=125695>Question 125695</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve:  6/i - 8/8-i. Combine and write the answer in standard form. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #92083 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=92083\">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=6%2Fi+-+8%2F%288-i%29 ALIGN=MIDDLE  ALT=\"6%2Fi+-+8%2F%288-i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The first thing to do is rationalize the denominators, i.e. get the i out of each denominator and then you will be able to find a LCD to allow you to add the fractions.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The first fraction is easy, you just multiply by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%2Fi ALIGN=MIDDLE  ALT=\"i%2Fi\"   DISABLED_style= \"max-width:90%; height:auto;\" >, giving you <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6i%2F1 ALIGN=MIDDLE  ALT=\"-6i%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (remember <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2=-1 ALIGN=MIDDLE  ALT=\"i%5E2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The other fraction requires you to remember the factorization of the difference of two squares.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-b%5E2=%28a%2Bb%29%28a-b%29 ALIGN=MIDDLE  ALT=\"a%5E2-b%5E2=%28a%2Bb%29%28a-b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Using this, we could multiply the denominator of the second fraction, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8-i ALIGN=MIDDLE  ALT=\"8-i\"   DISABLED_style= \"max-width:90%; height:auto;\" > by its conjugate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2Bi ALIGN=MIDDLE  ALT=\"8%2Bi\"   DISABLED_style= \"max-width:90%; height:auto;\" > to obtain <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%5E2-i%5E2=64%2B1=65 ALIGN=MIDDLE  ALT=\"8%5E2-i%5E2=64%2B1=65\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but to do that we also have to multiply the numerator by the same thing.  The result is that the second fraction looks like<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%288%288%2Bi%29%29%2F65 ALIGN=MIDDLE  ALT=\"-%288%288%2Bi%29%29%2F65\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Putting it all together we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%286i%2F1%29-%288%288%2Bi%29%29%2F65 ALIGN=MIDDLE  ALT=\"-%286i%2F1%29-%288%288%2Bi%29%29%2F65\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "65 is clearly the LCD, so\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-390i-64-8i%29%2F65=red%28%28-64%2F65%29-%28398i%2F65%29%29 ALIGN=MIDDLE  ALT=\"%28-390i-64-8i%29%2F65=red%28%28-64%2F65%29-%28398i%2F65%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );