Question

the denomination of a fraction is 1 more than its numerator . three times of the fraction is 1 less than twice of its reciprocal . find the fraction​

Answer 1

Answer:

2/3

Step-by-step explanation:

let x and y be the numerator and denominator

given that, y = x + 1   => x = y-1

also, 3(x/y) = 2(y/x) - 1

         3x / y  = (2y-x) / x

        3x² = 2y² - xy

=> 3x² = 2(x+1)² - x(x+1)

=> 3x² = 2(x²+1+2x) - x²-x

=> 3x² = 2x²+2+4x - x²-x

=> 3x²-2x²+ x² = 2+3x

=> 2x²-3x-2 = 0

=> 2x²-4x + x -2 = 0

=> 2x (x-2) + (x-2) = 0

=> (x-2)(2x+1) = 0

=> either x-2 = 0    or 2x+1 = 0

=> either x = 2 or x = -1/2

=> either y = 2+1 =3  or y =  (-1/2) + 1 = 1/2

=> the fraction is either 2/3 or (-1/2) / (1/2) =