Let the required fraction be x/y .
Then, we have: x+2/y = 1/2
⇒ 2(x + 2) = y
⇒ 2x + 4 = y
⇒2x - y = -4 ……(i)
Again, x/y−1 = 1/3
⇒3x = 1(y – 1)
⇒3x – y = -1 ……(ii)
On subtracting (i) from (ii), we get:
x = (-1 + 4) = 3
On substituting x = 3 in (i), we get:
2 × 3 – y = -4
⇒ 6 – y = -4
⇒ y = (6 + 4) = 10
∴ x = 3 and y = 10
Hence, the required fraction is 3/10