document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=866131>Question 866131</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In an unknown fraction the denominator is one more than twice the numerator.When 2 (1/10) is added to this fraction,the result is equal to the reciprocal of the unknown fraction.find the unkown fraction. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #522107 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=522107\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In an unknown fraction the denominator is one more than twice the numerator.<BR>\n" );
document.write( "When 2 (1/10) is added to this fraction,the result is equal to the reciprocal of the unknown fraction.<BR>\n" );
document.write( "find the unknown fraction.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let x = the numerator of the unknown fraction<BR>\n" );
document.write( "then \"the denominator is one more than twice the numerator\", therefore:<BR>\n" );
document.write( "(2x+1) = the denominator<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Change 2<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F10 ALIGN=MIDDLE  ALT=\"1%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21%2F10 ALIGN=MIDDLE  ALT=\"21%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"When 2 (1/10) is added to this fraction,the result is equal to the reciprocal of the unknown fraction.\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28%282x%2B1%29%29 ALIGN=MIDDLE  ALT=\"x%2F%28%282x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21%2F10 ALIGN=MIDDLE  ALT=\"21%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282x%2B1%29%29%2Fx ALIGN=MIDDLE  ALT=\"%28%282x%2B1%29%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "mult equation by 10x(2x+1), cancel the denominators and you have<BR>\n" );
document.write( "10x(x) + 21x(2x+1) = 10(2x+1)(2x+1)<BR>\n" );
document.write( "10x^2 + 42x^2 + 21x = 10(4x^2 + 4x + 1)<BR>\n" );
document.write( "52x^2 + 21x = 40x^2 + 40x + 10<BR>\n" );
document.write( "combine like terms on the left<BR>\n" );
document.write( "52x^2 - 40x^2 + 21x - 40x - 10 = 0<BR>\n" );
document.write( "12x^2 - 19x - 10 = 0<BR>\n" );
document.write( "Factors to <BR>\n" );
document.write( "(12x + 5)(x - 2) = 0<BR>\n" );
document.write( "only the positive integer makes sense here<BR>\n" );
document.write( "x = 2<BR>\n" );
document.write( "then the unknown fraction:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%28%282%282%29%2B1%29%29 ALIGN=MIDDLE  ALT=\"2%2F%28%282%282%29%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F5 ALIGN=MIDDLE  ALT=\"2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( ":\<BR>\n" );
document.write( "Check this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F5 ALIGN=MIDDLE  ALT=\"2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21%2F10 ALIGN=MIDDLE  ALT=\"21%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F2 ALIGN=MIDDLE  ALT=\"5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );