document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=151172>Question 151172</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the reciprocals of two consecutive even integers is 7/24. Find these integers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #111128 by </B><A HREF=/tutors/aboutme.mpl?userid=checkley77><B>checkley77(12844)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=checkley77><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=111128\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1/X+1/(X+2)=7/24<BR>\n" );
document.write( "(X+2+X)/X(X+2)=7/24<BR>\n" );
document.write( "(2X+2)/X^2+2X=7/24<BR>\n" );
document.write( "7(X^2+2X)=24(2X+2)<BR>\n" );
document.write( "7X^2+14X=48X+48<BR>\n" );
document.write( "7X^2+14X-48X-48=0<BR>\n" );
document.write( "7X^2-34X-48=0<BR>\n" );
document.write( "(7X+8)(X-6)=0<BR>\n" );
document.write( "X-6=0<BR>\n" );
document.write( "X=6 ANSWER FOR THE SMALLER INTEGER.<BR>\n" );
document.write( "6+2=8 FOR THE LARGER INTEGER.<BR>\n" );
document.write( "PROOF:<BR>\n" );
document.write( "1/6+1/8=7/24<BR>\n" );
document.write( "(8+6)/48=7/24<BR>\n" );
document.write( "14/48=7/24<BR>\n" );
document.write( "7/24=7/24<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );