document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=256445>Question 256445</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find two consecutive positive odd number given that difference between their reciprocals is 2/63  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #188545 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=188545\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> represent the smaller of the two consecutive odd integers.  Then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\,+\,2\"> must represent the next consecutive odd integer.\r<BR>\n" );
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document.write( "The reciprocal of the smaller is then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{1}{x}\">, and the reciprocal of the larger one is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{1}{x\,+\,2}\">.  Then the difference between the reciprocals is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{x}\ -\ \frac{1}{x\,+\,2}\ =\ \frac{2}{63}\">\r<BR>\n" );
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document.write( "Combine the fractions in the LHS using the common denominator <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x^2\,+\,2x\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\left(x\,+\2\right)\ -\ x}{x^2\,+\,2x}\ =\ \frac{2}{63}\">\r<BR>\n" );
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document.write( "Collect terms on the left:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{2}{x^2\,+\,2x}\ =\ \frac{2}{63}\">\r<BR>\n" );
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document.write( "Now we have two equal fractions with equal numerators -- therefore the denominators must be equal as well, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\,+\,2x\ =\ 63\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\,+\,2x\,-\,63\ =\ 0\">\r<BR>\n" );
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document.write( "Solve the factorable quadratic.  Discard the negative root.  The positive root will be the smaller of the two positive consecutive odd integers.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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