The sum of the numerator and denominator of a fraction is 4 more than twice the numerator.If the numerator and denominator are increased by 3, they are in the ratio 2:3.Determine the fraction.

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Solution

$l e t space t h e space f r a c t i o n space i s x over y a c c o r d i n g space t o space q u e s t i o n x plus y equals 2 x plus 4 x minus y equals negative 4 m u l t i p l y i n g space b y space 2 space f o r space s i m p l i c i t y 2 x minus 2 y equals negative 8......................... left parenthesis 1 right parenthesis c o n d i t i o n space 2 fraction numerator x plus 3 over denominator y plus 3 end fraction equals 2 over 3 3 x plus 9 equals 2 y plus 6 3 x minus 2 y equals negative 3......................... left parenthesis 2 right parenthesis s o l v i n g space e q u a t i o n s minus x equals negative 5 x equals 5 p u t t i n g space v a l u e space i n space e q space 1 space 10 minus 2 y equals negative 8 minus 2 y equals negative 18 y equals 9 h e n c e space t h e space f r a c t i o n space i s space 5 over 9$

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