the numerator of a certain fraction is four less then the denominator, if the numerator is doubled and the denominator is diminished by two, the sum of the original fraction and the new one is three. find the original fraction

Answer 1

old fraction: (x-4)/x

new fraction: 2(x-4)/(x-2)

and then it said:

(x-4)/x + 2(x-4)/(x-2) = 3

multiply each term by x(x-2)

(x-4)(x-2) + 2(x)(x-4) = 3x(x-2)
x^2 - 6x + 8 + 2x^2 - 8x = 3x^2 - 6x
-8x = -8
x = 1

the fraction was -3/1 ???
new fraction = -6/-1 = 6

The original fraction was -3/1 ?????

Check :
old fraction + new fraction
= -3 + 6 = 3 , it works

(poorly designed problem)