document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1023155>Question 1023155</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a certain positive fraction the denominator is greater than the numerator by  3 if 1 is subtracted from both the numerator and denominator the fraction is decreased by 1/14.find the fraction  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #638748 by </B><A HREF=/tutors/aboutme.mpl?userid=fractalier><B>fractalier(6550)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fractalier><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=fractalier><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=638748\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Call the original fraction<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2F+%28x%2B3%29 ALIGN=MIDDLE  ALT=\"x+%2F+%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then we add one to top and bottom and get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29+%2F+%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x-1%29+%2F+%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This fraction is 1/14 less than the original...thus we have to solve<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2F+%28x%2B3%29+-+1%2F14+=+%28x-1%29+%2F+%28x%2B2%29 ALIGN=MIDDLE  ALT=\"x+%2F+%28x%2B3%29+-+1%2F14+=+%28x-1%29+%2F+%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now multiply everything by the lowest common denominator...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2814%28x%2B2%29%28x%2B3%29%29%2A%28x%2F%28x%2B3%29+-+1%2F14%29+=+%2814%28x%2B2%29%28x%2B3%29%29%2A%28%28x-1%29+%2F+%28x%2B2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and we get<BR>\n" );
document.write( "14x(x+2) - (x+2)(x+3) = 14(x+3)(x-1)<BR>\n" );
document.write( "14x^2 + 28x - x^2 - 5x - 6 = 14x^2 + 28x - 42<BR>\n" );
document.write( "The 14x^2 and 28x cancel out...<BR>\n" );
document.write( "-x^2 - 5x - 6 = -42<BR>\n" );
document.write( "x^2 + 5x + 6 = 42<BR>\n" );
document.write( "x^2 + 5x - 36 = 0<BR>\n" );
document.write( "(x + 9)(x - 4) = 0<BR>\n" );
document.write( "x = -9 and x = 4<BR>\n" );
document.write( "The original fraction must be<BR>\n" );
document.write( "4/7. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );