document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=683653>Question 683653</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Good day to you.  My daughter is having a problem with algebra word problems, can you please help me, i am not so good at this either.\r<BR>\n" );
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document.write( "The denominator 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 #423648 by </B><A HREF=/tutors/aboutme.mpl?userid=ReadingBoosters><B>ReadingBoosters(3246)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ReadingBoosters><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=423648\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x is numerator<BR>\n" );
document.write( "y is denominator<BR>\n" );
document.write( "...<BR>\n" );
document.write( "y = 2x + 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+4%29%2F%28y-4%29+=+y%2Fx ALIGN=MIDDLE  ALT=\"%28x+%2B+4%29%2F%28y-4%29+=+y%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...<BR>\n" );
document.write( "Cross Multiply<BR>\n" );
document.write( "x(x+4) = y(y-4)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+4x+=+y%5E2+-+4y ALIGN=MIDDLE  ALT=\"x%5E2+%2B+4x+=+y%5E2+-+4y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+4x+-+y%5E2+%2B+4y++=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+4x+-+y%5E2+%2B+4y++=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+4x+-%282x%2B1%29%5E2+%2B+4%282x%2B1%29+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+4x+-%282x%2B1%29%5E2+%2B+4%282x%2B1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ==> substitution<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+4x+-%284x%5E2+%2B+4x+%2B+1%29+%2B+8x+%2B+4+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+4x+-%284x%5E2+%2B+4x+%2B+1%29+%2B+8x+%2B+4+=+0\"   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+%2B+4x+-+4x%5E2+-+4x+-+1+%2B+8x+%2B+4+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+4x+-+4x%5E2+-+4x+-+1+%2B+8x+%2B+4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%5E2+%2B+8x+%2B+3+=+0 ALIGN=MIDDLE  ALT=\"-3x%5E2+%2B+8x+%2B+3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%283x%5E2+-+8x+-+3%29=0 ALIGN=MIDDLE  ALT=\"-1%283x%5E2+-+8x+-+3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3x+1)(x-3)=0<BR>\n" );
document.write( "3x+1=0<BR>\n" );
document.write( "3x=-1<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F3 ALIGN=MIDDLE  ALT=\"-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x-3=0<BR>\n" );
document.write( "x = 3<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Using x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F3 ALIGN=MIDDLE  ALT=\"-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B1+=+2%28-1%2F3%29+%2B+1+=+-2%2F3+%2B+1+=+-2%2F3+%2B+3%2F3+=+1%2F3 ALIGN=MIDDLE  ALT=\"2x%2B1+=+2%28-1%2F3%29+%2B+1+=+-2%2F3+%2B+1+=+-2%2F3+%2B+3%2F3+=+1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Original fraction<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28%28-1%2F3%29%2F%281%2F3%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28%28-1%2F3%29%2F%281%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2F3%29%283%29+=+-1 ALIGN=MIDDLE  ALT=\"%28-1%2F3%29%283%29+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...<BR>\n" );
document.write( "Using x = 3<BR>\n" );
document.write( "y = 2x + 1 = 2(3) + 1 = 6 +1 = 7<BR>\n" );
document.write( "Original fraction<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%283%2F7%29 ALIGN=MIDDLE  ALT=\"highlight_green%283%2F7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...<BR>\n" );
document.write( "Testing both originals<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Checking <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2F3%29%2F%281%2F3%29 ALIGN=MIDDLE  ALT=\"%28-1%2F3%29%2F%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is -1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2B4%29%2F%281-4%29+=+3%2F-3+=+-1 ALIGN=MIDDLE  ALT=\"%28-1%2B4%29%2F%281-4%29+=+3%2F-3+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "it works! <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F1 ALIGN=MIDDLE  ALT=\"-1%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F-1 ALIGN=MIDDLE  ALT=\"1%2F-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > are reciprocals<BR>\n" );
document.write( "...<BR>\n" );
document.write( "checking <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F7 ALIGN=MIDDLE  ALT=\"3%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2B4%29%2F%287-4%29+=+7%2F3 ALIGN=MIDDLE  ALT=\"%283%2B4%29%2F%287-4%29+=+7%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F7 ALIGN=MIDDLE  ALT=\"3%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F3 ALIGN=MIDDLE  ALT=\"7%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > are reciprocals<BR>\n" );
document.write( "it is correct!<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Ultimately, there are two original fractions that qualify<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2F3%29%2F%281%2F3%29 ALIGN=MIDDLE  ALT=\"%28-1%2F3%29%2F%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F7 ALIGN=MIDDLE  ALT=\"3%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "..............................<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );