Let the numerator be x and the denominator be y Then, (x+y)2=289 ⇒x+y=17 …(1) Again,
3x+1
2y−2
=
2
1
3x+1=4y−1 3x−4y=−4−1 3x−4y=−5 …(2) Multiplying equation (1) by 3, 3x+3y=51 ....(3) From equation (2) and (3), we get 7y=56⇒y=8 ⇒x=9 So, the required fraction =