document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=32245>Question 32245</A>: <I><SPAN STYLE=\"word-break: break-all;\"> PROVE ALGEBRAICALLY THAT: ( (xy) / (1+(xz)) ) > ( ((xy)+(ab)) / (1 + (xz) + (ac)) ) REDUCES TO: (b/c) < ( (xy) / (1+(xz)) ). <BR>\n" );
document.write( "I HAVE NO IDEA WHERE TO EVEN START!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #18879 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=18879\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> PROVE ALGEBRAICALLY THAT: ( (xy) / (1+(xz)) ) > ( ((xy)+(ab)) / (1 + (xz) + (ac)) ) REDUCES TO: (b/c) < ( (xy) / (1+(xz)) ). <BR>\n" );
document.write( "I HAVE NO IDEA WHERE TO EVEN START!!<BR>\n" );
document.write( "DONT GET SCARED!KEEP UP THE SPIRIT.WE SHOULD LEARN HOWTO REMOVE THE VEILS OR CAMOUFLAGE TO LOOK AT THE REAL FRUIT.<BR>\n" );
document.write( "FOR THIS PURPOSE WE USE ONION PEEL APPROACH...REMOVE THE OUTR LAYERS ONE BY ONE...AND BUILDING BLOCKS..WE TRY TO LEARN FROM SMALL THINGS TO BIG THINGS.<BR>\n" );
document.write( "HERE THERE ARE BIG EXPRESSIONS..LET US SIMPLIFY BY NEW SYMBOLS.<BR>\n" );
document.write( "LET US CALL L= ( (xy) / (1+(xz)) )......AND M = ( ((xy)+(ab)) / (1 + (xz) + (ac))<BR>\n" );
document.write( "AND K = (b/c).....HENCE GIVEN L > M , TST.....K < L..........<BR>\n" );
document.write( "LET US STUDY SOME EXAMPLES...SUPPOSE \r<BR>\n" );
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document.write( "IF L=4/2=NUMBER GREATER THAN 1...THEN YOU CAN EASILY SEE THAT ADDING SAME NUMBER...SAY 2 TO NR AND DR WILL MAKE THE NEW NUMBER (4+2)/(2+2)=6/4=3/2 SMALLER.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "IF L=4/2=NUMBER GREATER THAN 1...THEN YOU CAN EASILY SEE THAT SUBTRACTINGING SAME NUMBER...SAY 1 FROM NR AND DR WILL MAKE THE NEW NUMBER (4-1)/(2-1)=3/1=3 BIGGER.\r<BR>\n" );
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document.write( "IF L=2/4=NUMBER SMALLER THAN 1...THEN YOU CAN EASILY SEE THAT ADDING SAME NUMBER...SAY 2 TO NR AND DR WILL MAKE THE NEW NUMBER (2+2)/(4+2)=4/6=2/3 BIGGER.\r<BR>\n" );
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document.write( "IF L=2/4=NUMBER SMALLER THAN 1...THEN YOU CAN EASILY SEE THAT SUBTRACTING SAME NUMBER...SAY 1 FROM NR AND DR WILL MAKE THE NEW NUMBER (2-1)/(4-1)=1/3= SMALLER.<BR>\n" );
document.write( "  THIS IS FUNDAMENTAL PROPERTY OF FRACTIONS. <BR>\n" );
document.write( "    NOW WE HAVE <BR>\n" );
document.write( "K=B/C..OR..B=KC....SO AB =KAC<BR>\n" );
document.write( "WE ARE GIVEN THAT<BR>\n" );
document.write( "L>(L+KAC)/(1+AC).....FROM THIS AND ABOVE PROPERTIES OF FRACTIONS,WE SEE THAT <BR>\n" );
document.write( "IF L >1...THEN AC IS POSITIVE...AND IF L< 1 THEN AC IS NEGATIVE.<BR>\n" );
document.write( "I SHALL SHOW YOU THE PROOF FOR THE FIRST ALTERNATIVE AND YOU CAN DO FOR THE SECOND ALTERNATIVE.<BR>\n" );
document.write( "L >1 AND AC IS POSITIVE<BR>\n" );
document.write( " L-(L+KAC)/(1+AC)>0<BR>\n" );
document.write( "(L+LAC-L-KAC)/(1+AC)>0<BR>\n" );
document.write( "AC(L-K)>0...SINCE AC IS POSITIVE AND HENCE 1+AC IS POSITIVE.<BR>\n" );
document.write( "L-K>0........SINCE AC IS POSITIVE<BR>\n" );
document.write( "L>K...OR K<L...PROVED. </SPAN>\n" );
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