document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192891>Question 1192891</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the numerator of a fraction is 1 less than the denominator. <BR>\n" );
document.write( "when both numerator and denominator are increased by 2, <BR>\n" );
document.write( "the fraction is increased 1/12`find the original fraction<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #824828 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=824828\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Your statement of the problem is not clear.  When the problem says the fraction is \"increased by 1/12\", it is not clear whether that is an increase by a FACTOR of 1/12 or an increase of an ADDED 1/12.<br><BR>\n" );
document.write( "The other tutor interpreted the meaning to be an increase by a factor of 1/12, which makes the problem have no solution.<br><BR>\n" );
document.write( "The problem has a solution if the increase is an added 1/12.<br><BR>\n" );
document.write( "Let the denominator of the original fraction be x; then the two fractions are (x-1)/x and (x+1)/(x+2).<br><BR>\n" );
document.write( "The second fraction is 1/12 MORE than the first:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%2F%28x%2B2%29-%28x-1%29%2Fx=1%2F12 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%2F%28x%2B2%29-%28x-1%29%2Fx=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=%28x%2B1%29%28x%29-%28x-1%29%28x%2B2%29=%28x%28x%2B2%29%29%2F12 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%28x%29-%28x-1%29%28x%2B2%29=%28x%28x%2B2%29%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2Bx%29-%28x%5E2%2Bx-2%29=%28x%5E2%2B2x%29%2F12 ALIGN=MIDDLE  ALT=\"%28x%5E2%2Bx%29-%28x%5E2%2Bx-2%29=%28x%5E2%2B2x%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=%28x%5E2%2B2x%29%2F12 ALIGN=MIDDLE  ALT=\"2=%28x%5E2%2B2x%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x=24 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x=24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x-24=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x-24=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B6%29%28x-4%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B6%29%28x-4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6 ALIGN=MIDDLE  ALT=\"x=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "If we choose the positive solution, then the original fraction is 3/4 and the new fraction is 5/6, and 5/6 - 3/4 = 10/12 - 9/12 = 1/12; the conditions of the problem are satisfied.<br><BR>\n" );
document.write( "If we choose the negative solution, the the original fraction is (-7)/(-6) and the new fraction is (-5)/(-4); and (-5)/(-4) - (-7)/(-6) = 5/4 - 7/6 = 15/12 = 14/12 = 1/12; again the conditions of the problem are satisfied.<br><BR>\n" );
document.write( "So the original fraction could be either 3/4 or (-7)/(-6).  However, the format of the second \"solution\" is not standard, so....<br><BR>\n" );
document.write( "ANSWER: The original fraction was 3/4<br><BR>\n" );
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