document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=481709>Question 481709</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (x+y)/(3a-b)=(y+z)/(3b-c)=(z+x)/(3c-a)<BR>\n" );
document.write( "prove that <BR>\n" );
document.write( "(x+y+z)/(a+b+c)=(ax+by+cz)/(a^2+b^2+c^2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #329857 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=329857\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have to apply the rule of identities.<BR>\n" );
document.write( " <BR>\n" );
document.write( "a1/b1 = a2/b2 = a3/b3 <BR>\n" );
document.write( "= (a1+a2+a3)/(b1+b2+b3) ---- 1<BR>\n" );
document.write( " = (a1-a2+a3)/(b1-b2+b3) ---- 2<BR>\n" );
document.write( " = (a2-a3+a1)/(b2-b3+b1) ---- 3<BR>\n" );
document.write( " = (a3-a1+a2)/(b3-b1+b2) ---- 4<BR>\n" );
document.write( "..............<BR>\n" );
document.write( " <BR>\n" );
document.write( "apply  to the given equations:<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%29%2F%283a-b%29+=+%28y%2Bz%29%2F%283b-c%29+=+%28z%2Bx%29%2F%283c-a%29 ALIGN=MIDDLE  ALT=\"%28x%2By%29%2F%283a-b%29+=+%28y%2Bz%29%2F%283b-c%29+=+%28z%2Bx%29%2F%283c-a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%2By%2Bz%2Bz%2Bx%29+%2F+%283a-b%2B3b-c%2B3c-a%29 ALIGN=MIDDLE  ALT=\"%28x%2By%2By%2Bz%2Bz%2Bx%29+%2F+%283a-b%2B3b-c%2B3c-a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----using (1)<BR>\n" );
document.write( " = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%2Bz%29%2F%28a%2Bb%2Bc%29 ALIGN=MIDDLE  ALT=\"%28x%2By%2Bz%29%2F%28a%2Bb%2Bc%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By-y-z%2Bz%2Bx%29+%2F+%283a-b-3b%2Bc%2B3c-a%29 ALIGN=MIDDLE  ALT=\"%28x%2By-y-z%2Bz%2Bx%29+%2F+%283a-b-3b%2Bc%2B3c-a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---- by (2)<BR>\n" );
document.write( " = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2F+%282a+-+4b+%2B+4c%29 ALIGN=MIDDLE  ALT=\"2x+%2F+%282a+-+4b+%2B+4c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2F+%28a-2b%2B2c%29 ALIGN=MIDDLE  ALT=\"x+%2F+%28a-2b%2B2c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax+%2F+%28a%5E2+-+2ab+%2B+2ca%29 ALIGN=MIDDLE  ALT=\"ax+%2F+%28a%5E2+-+2ab+%2B+2ca%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---- result A<BR>\n" );
document.write( " <BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2Bz-z-x%2Bx%2By%29+%2F+%283b-c-3c%2Ba%2B3a-b%29 ALIGN=MIDDLE  ALT=\"%28y%2Bz-z-x%2Bx%2By%29+%2F+%283b-c-3c%2Ba%2B3a-b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---- by (3)<BR>\n" );
document.write( " = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y+%2F+%282b+-+4c+%2B+4a%29 ALIGN=MIDDLE  ALT=\"2y+%2F+%282b+-+4c+%2B+4a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%2F+%28b-2c%2B2a%29 ALIGN=MIDDLE  ALT=\"y+%2F+%28b-2c%2B2a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=by+%2F+%28b%5E2+-+2bc+%2B+2ab%29 ALIGN=MIDDLE  ALT=\"by+%2F+%28b%5E2+-+2bc+%2B+2ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---- result B<BR>\n" );
document.write( " <BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28z%2Bx-x-y%2By%2Bz%29+%2F+%283c-a-3a%2Bb%2B3b-c%29 ALIGN=MIDDLE  ALT=\"%28z%2Bx-x-y%2By%2Bz%29+%2F+%283c-a-3a%2Bb%2B3b-c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---- by(4)<BR>\n" );
document.write( " = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2z+%2F+%282c+-+4a+%2B+4b%29 ALIGN=MIDDLE  ALT=\"2z+%2F+%282c+-+4a+%2B+4b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+%2F+%28c-2a-2b%29 ALIGN=MIDDLE  ALT=\"z+%2F+%28c-2a-2b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cz+%2F+%28c%5E2+-+2ca+%2B+2bc%29 ALIGN=MIDDLE  ALT=\"cz+%2F+%28c%5E2+-+2ca+%2B+2bc%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---- result C<BR>\n" );
document.write( " <BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28ax+%2B+by+%2Bcz%29+%2F+%28+%28a%5E2+-+2ab+%2B+2ca%29+%2B+%28b%5E2+-+2bc+%2B+2ab%29+%2B+%28c%5E2+-+2ca+%2B+2bc%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > -------- by adding results A,B,C<BR>\n" );
document.write( " <BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28ax+%2B+by+%2Bcz%29+%2F+%28a%5E2+%2B+b%5E2+%2B+c%5E2%29 ALIGN=MIDDLE  ALT=\"%28ax+%2B+by+%2Bcz%29+%2F+%28a%5E2+%2B+b%5E2+%2B+c%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "m.ananth@hotmail.ca </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );