document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120905>Question 1120905</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The numerator of a fraction is 2 less than its denominator. If 3 is subtracted from the numerator and from the denominator, the new fraction obtained is 3/4. Find the fraction. </SPAN>\n" );
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document.write( "Using formal algebra....<br><BR>\n" );
document.write( "Let the original fraction be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"x%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "3 subtracted from both numerator and denominator makes the fraction <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"%28x-3%29%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "We want that new fraction to have the value 3/4:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%2F%28x-1%29+=+3%2F4 ALIGN=MIDDLE  ALT=\"%28x-3%29%2F%28x-1%29+=+3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x-3+=+4x-12 ALIGN=MIDDLE  ALT=\"3x-3+=+4x-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+9 ALIGN=MIDDLE  ALT=\"x+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The original fraction is x/(x+2) = 9/11.<br><BR>\n" );
document.write( "Using logical reasoning....<br><BR>\n" );
document.write( "When 3 is subtracted from both numerator and denominator, the numerator is still 2 less than the denominator.  So look for a fraction equivalent to 3/4 in which the numerator is 2 less than the denominator.<br><BR>\n" );
document.write( "In the fraction 3/4, the numerator is 1 less than the denominator; multiplying numerator and denominator by 2 will give us a fraction equivalent to 3/4 in which the numerator is 2 less than the denominator: 3/4 = 6/8.<br><BR>\n" );
document.write( "So 6/8 is the fraction after 3 has been subtracted from both numerator and denominator; that means the original fraction was 9/11. </SPAN>\n" );
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