document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=550003>Question 550003</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify by writing the expression as a single quotient in which only positive exponents appear. <BR>\n" );
document.write( "[<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2881-X%5E2%29%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"%2881-X%5E2%29%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4X%5E2%2881-X%5E2%29%5E%28-1%2F2%29 ALIGN=MIDDLE  ALT=\"4X%5E2%2881-X%5E2%29%5E%28-1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >]/<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81-X%5E2 ALIGN=MIDDLE  ALT=\"81-X%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #358293 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=358293\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> [(81-X^2)^(1/2) + 4X^2(81-X^2)^(-1/2)] /{81-X^2}<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Let (81-x^2) = m<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Substitute for simplicity's sake:<BR>\n" );
document.write( "----<BR>\n" );
document.write( "[ sqrt(m) + 4x^2/sqrt(m) ] / m<BR>\n" );
document.write( "---<BR>\n" );
document.write( "[m + 4x^2]/sqrt(m)/m<BR>\n" );
document.write( "---<BR>\n" );
document.write( "[m + 4x^2]/m^(3/2)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Substitute back to get:<BR>\n" );
document.write( "[(81-x^2) +4x^2]/(81-x^2)^(3/2)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "= [3x^2+81]/[81-x^2)^(3/2)<BR>\n" );
document.write( "=============================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "=========== </SPAN>\n" );
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