document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=373161>Question 373161</A>: <I><SPAN STYLE=\"word-break: break-all;\">  The difference of the reciprocals of two consecutive even integers is 1/12 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 #265656 by </B><A HREF=/tutors/aboutme.mpl?userid=CharlesG2><B>CharlesG2(834)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CharlesG2><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=265656\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The difference of the reciprocals of two consecutive even integers is 1/12 Find the Integers\r<BR>\n" );
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document.write( "let n be one integer<BR>\n" );
document.write( "let n + 2 be the next consecutive even integer<BR>\n" );
document.write( "1/n - 1/(n + 2) = 1/12<BR>\n" );
document.write( "12/n - 12/(n + 2) = 1<BR>\n" );
document.write( "12 - 12n/(n + 2) = n<BR>\n" );
document.write( "12(n + 2) - 12n = n(n + 2)<BR>\n" );
document.write( "12n + 24 - 12n = n^2 + 2n<BR>\n" );
document.write( "24 = n^2 + 2n<BR>\n" );
document.write( "0 = n^2 + 2n - 24<BR>\n" );
document.write( "0 = (n - 4)(n + 6) (by FOIL this same, 6n - 4n = 2n)<BR>\n" );
document.write( "n = 4 or n = -6<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "1/4 - 1/6 = 1/4 * 3/3 - 1/6 * 2/2 = 3/12 - 2/12 = 1/12, yes<BR>\n" );
document.write( "1/(-6) - 1/(-4) = -1/6 + 1/4 = -1/6 * 2/2 + 1/4 * 3/3 = -2/12 + 3/12 = 1/12, yes\r<BR>\n" );
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document.write( "4 and 6 or -6 and -4 are answers<BR>\n" );
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