document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120747>Question 1120747</A>: <I><SPAN STYLE=\"word-break: break-all;\"> We may define the three means (arithmetic, geometric, and harmonic) of two positive numbers a and b as <BR>\n" );
document.write( "A = (a+b)/2 <BR>\n" );
document.write( "G = &#8730;ab <BR>\n" );
document.write( "H = 2ab/ a+b, respectively \r<BR>\n" );
document.write( "\n" );
document.write( "c. show that 1/ H-a + 1/ H-b = 1/a + 1/b </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #737736 by </B><A HREF=/tutors/aboutme.mpl?userid=amarjeeth123><B>amarjeeth123(570)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=amarjeeth123><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=737736\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A = (a+b)/2<BR>\n" );
document.write( "G = &#8730;ab<BR>\n" );
document.write( "H = 2ab/ a+b<BR>\n" );
document.write( "H-a=(2ab/a+b)-a=(2ab-a^2-ab/a+b)=(ab-a^2/a+b)<BR>\n" );
document.write( "H-b=(2ab/a+b)-b=(2ab-ab-b^2)/(a+b)=(ab-b^2/a+b)<BR>\n" );
document.write( "1/H-a=a+b/ab-a^2<BR>\n" );
document.write( "1/H-b=a+b/ab-b^2<BR>\n" );
document.write( "1/H-a+1/H-b=a+b(1/a(b-a)+1/b(a-b))=a+b(1/b(a-b)-1/a(a-b))=a+b(a-b/ab(a-b))=a+b/ab=1/a+1/b<BR>\n" );
document.write( "Hence proved. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );