document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=269624>Question 269624</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The difference of the reciprocals of two consecutive integers is 1/42. Find the integers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #197600 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=197600\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The difference of the reciprocals of two consecutive integers is 1/42. Find the integers.<BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "1st: x<BR>\n" );
document.write( "2nd: x+1<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Equation:<BR>\n" );
document.write( "1/x - 1/(x+1) = 1/42<BR>\n" );
document.write( "[(x+1) - x]/[x(x+1)] = 1/42<BR>\n" );
document.write( "---<BR>\n" );
document.write( "1/(x^2+x) = 1/42<BR>\n" );
document.write( "----<BR>\n" );
document.write( "x^2+x = 42<BR>\n" );
document.write( "x^2 + x -42 = 0<BR>\n" );
document.write( "Factor:<BR>\n" );
document.write( "(x+7)(x-6) = 0<BR>\n" );
document.write( "x = -7 or x = 6<BR>\n" );
document.write( "---<BR>\n" );
document.write( "If x = -7, x+1 = -6<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "If x = 6, x+1 = 7<BR>\n" );
document.write( "=======================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );