document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1042996>Question 1042996</A>: <I><SPAN STYLE=\"word-break: break-all;\"> prove, if x,y &#8712; Q <BR>\n" );
document.write( "then there are integers a,b,c <BR>\n" );
document.write( "such that x=a/c and y=b/c </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #658065 by </B><A HREF=/tutors/aboutme.mpl?userid=LinnW><B>LinnW(1048)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=LinnW><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=LinnW><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=658065\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since x and y are rational there exist<BR>\n" );
document.write( "integers d and e such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+d%2Fe ALIGN=MIDDLE  ALT=\"x+=+d%2Fe\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and integers f and g such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+f%2Fg ALIGN=MIDDLE  ALT=\"y+=+f%2Fg\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Notice that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+d%2Fe ALIGN=MIDDLE  ALT=\"x+=+d%2Fe\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28d%2Fe%29%28g%2Fg%29 ALIGN=MIDDLE  ALT=\"x+=+%28d%2Fe%29%28g%2Fg%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+dg%2Feg ALIGN=MIDDLE  ALT=\"x+=+dg%2Feg\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+f%2Fg ALIGN=MIDDLE  ALT=\"y+=+f%2Fg\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28f%2Fg%29%28e%2Fe%29 ALIGN=MIDDLE  ALT=\"y+=+%28f%2Fg%29%28e%2Fe%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+fe%2Feg ALIGN=MIDDLE  ALT=\"y+=+fe%2Feg\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+dg%2Feg ALIGN=MIDDLE  ALT=\"x+=+dg%2Feg\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+fe%2Feg ALIGN=MIDDLE  ALT=\"y+=+fe%2Feg\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since the product of two integers is an integer,<BR>\n" );
document.write( "we can set c = eg where c is an integer<BR>\n" );
document.write( "set a = dg where a is an integer<BR>\n" );
document.write( "set b = fe where b is an integer<BR>\n" );
document.write( "Substituting we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+a%2Fc ALIGN=MIDDLE  ALT=\"x+=+a%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+b%2Fc ALIGN=MIDDLE  ALT=\"y+=+b%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );