document.write( "Question 1190756: the denominator of a fraction is 4 more than the numerator. If 3 is added to both the numerator and denominator, the new fraction is 2/3. What is the original fraction? \n" ); document.write( "
Algebra.Com's Answer #822464 by Theo(13342)\"\" \"About 
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let x be the numerator and y be the denominator.
\n" ); document.write( "the fraction is x/y.
\n" ); document.write( "you are given that the denominator is 4 more than the numerator.
\n" ); document.write( "xince y = x + 4, the fraction becomes:
\n" ); document.write( "x/(x+4)
\n" ); document.write( "you are given that when 3 is added to both the numerator and the denominator, the fraction is 2/3.
\n" ); document.write( "this gets you:
\n" ); document.write( "(x + 3) / (x + 4 + 3) = 2/3
\n" ); document.write( "simplify to get:
\n" ); document.write( "(x + 3) / (x + 7) = 2/3
\n" ); document.write( "cross multiply to get:
\n" ); document.write( "3 * (x + 3) = 2 * (x + 7)
\n" ); document.write( "simplify to get:
\n" ); document.write( "3x + 9 = 2x + 14
\n" ); document.write( "subtract 2x from both sides and subtract 9 from both sides to get:
\n" ); document.write( "x = 5
\n" ); document.write( "since y = 4 more than that, you get:
\n" ); document.write( "x = 5
\n" ); document.write( "y = 9
\n" ); document.write( "the original fraction is x/y = 5/9
\n" ); document.write( "add 3 to the numerator and he denominator to get 8/12 which is equal to 2/3.
\n" ); document.write( "this confirms the solution is correct.
\n" ); document.write( "the solution is that the original fraction is 5/9.
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