Let, the numerator x=11−y Denominator =y Sum of numerator and denominator = 11 Now,
x+2
y+2
=
x
y
+
1
24
x+2
y+2
=
24x+y
24y
24xy+48y=24xy+48x+y2+2y y2+48x−46y=0 y2+48(11−y)−46y=0 y2−48y−46y+528=0 y2−94y+528=0 y2−88y−6y+528=0 y(y−88)−6(y−88)=0 y=6,88 y=88 is not possible so y=6 Now x=11−y=11−6=5 Difference of numerator and denominator is 1.