document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=191912>Question 191912</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The difference between the reciprocal of two consecutive positive even number is 1/12. Find the two numbers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #144007 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=144007\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The difference between the reciprocal of two consecutive positive even number is 1/12. Find the two numbers.:<BR>\n" );
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document.write( "Two numbers x, (x+2)\r<BR>\n" );
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document.write( "The equation for the above statement:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"1%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx ALIGN=MIDDLE  ALT=\"1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F12 ALIGN=MIDDLE  ALT=\"1%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ";<BR>\n" );
document.write( "Multiply equation by 12x(x+2)<BR>\n" );
document.write( "12x(x+2)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"1%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - 12x(x+2)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx ALIGN=MIDDLE  ALT=\"1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 12x(x+2)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F12 ALIGN=MIDDLE  ALT=\"1%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cancel out the denominators and you have:<BR>\n" );
document.write( "12x - 12(x+2) = x(x+2)<BR>\n" );
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document.write( "12x - 12x + 24 = x^2 + 2x<BR>\n" );
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document.write( "0 = x^2 + 2x - 24; a quadratic equation<BR>\n" );
document.write( "Factors to:<BR>\n" );
document.write( "(x+6)(x-4) = 0<BR>\n" );
document.write( "positive solution<BR>\n" );
document.write( "x = 4, and 6 are the two numbers<BR>\n" );
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document.write( "Check solution in our original equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F12 ALIGN=MIDDLE  ALT=\"1%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F12 ALIGN=MIDDLE  ALT=\"3%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F12 ALIGN=MIDDLE  ALT=\"2%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F12 ALIGN=MIDDLE  ALT=\"1%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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