document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=317101>Question 317101</A>: <I><SPAN STYLE=\"word-break: break-all;\"> from special relativity, I can get most of the way apart from the very last step<BR>\n" );
document.write( "how do you simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c%2Fsqrt%28c%5E2+-+v%5E2%29+ ALIGN=MIDDLE  ALT=\"+c%2Fsqrt%28c%5E2+-+v%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <BR>\n" );
document.write( "the answer should be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2Fsqrt%281+-+v%5E2%2Fc%5E2%29+ ALIGN=MIDDLE  ALT=\"+1%2Fsqrt%281+-+v%5E2%2Fc%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "but I don't see how it's done\r<BR>\n" );
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document.write( "thanks<BR>\n" );
document.write( "John\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 #227018 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=227018\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It's not much of a simplification (in my opinion) as the expression doesn't get any simpler, but here it goes...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c%2Fsqrt%28c%5E2+-+v%5E2%29+ ALIGN=MIDDLE  ALT=\"+c%2Fsqrt%28c%5E2+-+v%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28c%2Fc%29%2F%28sqrt%28c%5E2+-+v%5E2%29%2Fc%29+ ALIGN=MIDDLE  ALT=\"+%28c%2Fc%29%2F%28sqrt%28c%5E2+-+v%5E2%29%2Fc%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both the numerator and the denominator by 'c'\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F%28sqrt%28c%5E2+-+v%5E2%29%2Fc%29+ ALIGN=MIDDLE  ALT=\"+1%2F%28sqrt%28c%5E2+-+v%5E2%29%2Fc%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2Fc ALIGN=MIDDLE  ALT=\"c%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F%28sqrt%28c%5E2+-+v%5E2%29%2Fsqrt%28c%5E2%29%29+ ALIGN=MIDDLE  ALT=\"+1%2F%28sqrt%28c%5E2+-+v%5E2%29%2Fsqrt%28c%5E2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28c%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28c%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Note: this implies that 'c' is a non-negative number, which it is.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F%28sqrt%28%28c%5E2+-+v%5E2%29%2F%28c%5E2%29%29%29+ ALIGN=MIDDLE  ALT=\"+1%2F%28sqrt%28%28c%5E2+-+v%5E2%29%2F%28c%5E2%29%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the lower square roots using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29%2Fsqrt%28y%29=sqrt%28x%2Fy%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%29%2Fsqrt%28y%29=sqrt%28x%2Fy%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=+1%2F%28sqrt%28%28c%5E2%29%2F%28c%5E2%29+-+%28v%5E2%29%2F%28c%5E2%29%29%29+ ALIGN=MIDDLE  ALT=\"+1%2F%28sqrt%28%28c%5E2%29%2F%28c%5E2%29+-+%28v%5E2%29%2F%28c%5E2%29%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the lower inner fraction.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F%28sqrt%281+-+%28v%5E2%29%2F%28c%5E2%29%29%29+ ALIGN=MIDDLE  ALT=\"+1%2F%28sqrt%281+-+%28v%5E2%29%2F%28c%5E2%29%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28c%5E2%29%2F%28c%5E2%29 ALIGN=MIDDLE  ALT=\"%28c%5E2%29%2F%28c%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 1.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c%2Fsqrt%28c%5E2+-+v%5E2%29+=+1%2F%28sqrt%281+-+%28v%5E2%29%2F%28c%5E2%29%29%29+ ALIGN=MIDDLE  ALT=\"+c%2Fsqrt%28c%5E2+-+v%5E2%29+=+1%2F%28sqrt%281+-+%28v%5E2%29%2F%28c%5E2%29%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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