The denominator of a fraction in its simplest form is greater than the numerator by 3. if 7 is added to the numerator, and 5 added to the denominator, then the fraction itself is increased by 1/2 . find the original fraction.

let numerator be x and denominator be y

x = y-3...eqn 1

{(x +7)/ (y+5) } - x/y = 1/2... eqn 2

expandin eqn 2...

2y(x+7) - 2x(y+5) = y(y+5)

=》 2xy + 14y - 2xy -10x = y^2 + 5y

=》 14y - 10x = y^2 + 5y...eqn 3

subst x = y-3 in eqn 3

=》 y^2 + 5y - 14y + 10y -30 = 0

=》 y^2 + y - 30 = 0

solving the eqn

y = 5 thus x = 2

subst y = x+3 into eqn 2

2x +14 = x +8

x = -6

1/4 because there is 4 grades.

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