Problema Solution
FIND two fractions with the same denominator, one positive and one negative, whose difference is 2/3
Answer provided by our tutors
Let 'x' represent the denominator and let the positive fraction be 1/x, and also x > 0.
Let 'y/x' represent the negative fraction, y < 0.
The difference between the fractions is 2/3.
Positive Fraction - Negative Fraction = 2/3
1/x - y/x = 2/3
(1 - y)/x = 2/3
For x = 3 we have 1 - y = 2 that is y = -1.
Two such fractions are 1/3 and -1/3.
Indeed:
1/3 - (-1/3) = 1/3 + 1/3 = 2/3.