In an unknown fraction the denominator is one more than twice the numerator. When 2.1 is added to this fraction.the answer is equal to the reciprocal of the unknown fraction. Find the unknown fraction

Answer 1

original fraction = x/(2x+1)

x/(2x+1) + 2.1 = (2x+1)/x

multiply by x(2x+1)
x^2 + 2.1x(2x+1) = (2x+1)(2x+1)
x^2 + 4.2x^2 + 2.1x = 4x^2 + 4x + 1

1.2x^2 - 1.9x - 1 = 0
12x^2 - 19x - 10 = 0
(x - 2)(12x + 5) = 0
x = 2 or x = -5/12

since the terms of a fraction are integers,
we use x = 2
and the original fraction was 2/5

check:
2/5 + 1.2 = .4 + 2.1 = 2.5
and 2.5 = 25/10 = 5/2 , the reciprocal of the original fraction