The numerator of a fraction is four less than the denominator The sum of the fraction and its reciprocal is 5/2 Find the numerator and denominator if each is a positive integer

Answer 1

denominator --- x
numerator ---- x-4

(x/x-4) + (x-4)/x = 5/2
times 2x(x-4)

2x^2 + 2(x-4)^2 = 5x(x-4)
2x^2 + 2x^2 - 16x + 32 = 5x^2 - 20x
-x^2 + 4x + 32 = 0
x^2 -4x - 32 = 0
(x-8)(x+4) = 0
x = 8 or x = -4 , but x was positive

so x = 8

so original fraction was 4/8 or 1/2

check:
1/2 + 2/1 = 2 1/2 = 5/2

Answer 2

the denominator of a fraction is 1 more than the numerator.the sum of the fraction and its reciprocal is 2 1/30.find the fraction