document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=683618>Question 683618</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Good day!  Kindly help me with this word problem.\r<BR>\n" );
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document.write( "The denominators of a fraction is 1 more than twice the numerator.  If 4 is added to the numerator and subtracted from the denominator, the result is the reciprocal of the fraction.  Find the original fraction.\r<BR>\n" );
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document.write( "Thank you very much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #423710 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=423710\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2Fd ALIGN=MIDDLE  ALT=\"n%2Fd\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the original fraction<BR>\n" );
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document.write( "The denominators of a fraction is 1 more than twice the numerator.<BR>\n" );
document.write( "d = 2n + 1<BR>\n" );
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document.write( "If 4 is added to the numerator and subtracted from the denominator, the result is the reciprocal of the fraction.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28n%2B4%29%29%2F%28%28d-4%29%29 ALIGN=MIDDLE  ALT=\"%28%28n%2B4%29%29%2F%28%28d-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fn ALIGN=MIDDLE  ALT=\"d%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cross multiply<BR>\n" );
document.write( "d(d-4) = n(n+4)<BR>\n" );
document.write( "d^2 - 4d = n^2 + 4n<BR>\n" );
document.write( "Replace d with (2n+1)<BR>\n" );
document.write( "(2n+1)^2 - 4(2n+1) = n^2 + 4n<BR>\n" );
document.write( "4n^2 + 4n + 1 - 8n - 4 = n^2 + 4n<BR>\n" );
document.write( "4n^2 - 4n - 3 = n^2 + 4n<BR>\n" );
document.write( "4n^2 - n^2 - 4n - 4n - 3 = 0<BR>\n" );
document.write( "a quadratic equation<BR>\n" );
document.write( "3n^2 - 8n - 3 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(3n+1)(n-3) = 0<BR>\n" );
document.write( "The positive solution is all we want here<BR>\n" );
document.write( "n = 3 is the original numerator<BR>\n" );
document.write( "and<BR>\n" );
document.write( "d = 2(3)+1<BR>\n" );
document.write( "d = 7 is the original denominator<BR>\n" );
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document.write( "You can check this in the given statement\r<BR>\n" );
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