document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=540520>Question 540520</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if the numerator of a certain fraction is increased by 2 and the denominator is increased by 1, the resulting fraction equals 1/2.  if, however, the numerator is increased by 1 and the denominator is decreased by 2, the resulting fraction equals 3/5.  Find the fraction </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #353758 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=353758\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the numerator<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the denominator<BR>\n" );
document.write( "given:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+a+%2B+2+%29+%2F+%28+b+%2B+1+%29+=+1%2F2+ ALIGN=MIDDLE  ALT=\"+%28+a+%2B+2+%29+%2F+%28+b+%2B+1+%29+=+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+a+%2B+1+%29+%2F+%28+b+-+2+%29+=+3%2F5+ ALIGN=MIDDLE  ALT=\"+%28+a+%2B+1+%29+%2F+%28+b+-+2+%29+=+3%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "Multiply both sides of (1) by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2A%28+b+%2B+1+%29+ ALIGN=MIDDLE  ALT=\"+2%2A%28+b+%2B+1+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2A%28+a+%2B+2+%29+=+b+%2B+1+ ALIGN=MIDDLE  ALT=\"+2%2A%28+a+%2B+2+%29+=+b+%2B+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2a+%2B+4+=+b+%2B+1+ ALIGN=MIDDLE  ALT=\"+2a+%2B+4+=+b+%2B+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2a+-+b+=+-3+ ALIGN=MIDDLE  ALT=\"+2a+-+b+=+-3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides of (2) by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5%2A%28+b+-+2+%29+ ALIGN=MIDDLE  ALT=\"+5%2A%28+b+-+2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5%2A%28+a+%2B+1+%29+=+3%2A%28+b+-+2+%29+ ALIGN=MIDDLE  ALT=\"+5%2A%28+a+%2B+1+%29+=+3%2A%28+b+-+2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5a+%2B+5+=+3b+-+6+ ALIGN=MIDDLE  ALT=\"+5a+%2B+5+=+3b+-+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5a+-+3b+=+-11+ ALIGN=MIDDLE  ALT=\"+5a+-+3b+=+-11+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "Multiply both sides of (1) by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "subtract (1) from (2)<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6a+-+3b+=+-9+ ALIGN=MIDDLE  ALT=\"+6a+-+3b+=+-9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5a+-+3b+=+-11+ ALIGN=MIDDLE  ALT=\"+5a+-+3b+=+-11+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-6a+%2B+3b+=+9+ ALIGN=MIDDLE  ALT=\"+-6a+%2B+3b+=+9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-a+=+-2+ ALIGN=MIDDLE  ALT=\"+-a+=+-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+2+ ALIGN=MIDDLE  ALT=\"+a+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and, since<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2a+-+b+=+-3+ ALIGN=MIDDLE  ALT=\"+2a+-+b+=+-3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2A2+-+b+=+-3+ ALIGN=MIDDLE  ALT=\"+2%2A2+-+b+=+-3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b+=+-7+ ALIGN=MIDDLE  ALT=\"+-b+=+-7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+7+ ALIGN=MIDDLE  ALT=\"+b+=+7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the fraction is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fb+=+2%2F7+ ALIGN=MIDDLE  ALT=\"a%2Fb+=+2%2F7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "check answer:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+2+%2B+2+%29+%2F+%28+7+%2B+1+%29+=+1%2F2+ ALIGN=MIDDLE  ALT=\"+%28+2+%2B+2+%29+%2F+%28+7+%2B+1+%29+=+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%2F8+=+1%2F2+ ALIGN=MIDDLE  ALT=\"+4%2F8+=+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F2+=+1%2F2+ ALIGN=MIDDLE  ALT=\"+1%2F2+=+1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+2+%2B+1+%29+%2F+%28+7+-+2+%29+=+3%2F5+ ALIGN=MIDDLE  ALT=\"+%28+2+%2B+1+%29+%2F+%28+7+-+2+%29+=+3%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%2F5+=+3%2F5+ ALIGN=MIDDLE  ALT=\"+3%2F5+=+3%2F5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );