Explanation

X/Y = 3/2 So X = 3Y/2

(X^2 + Y^2)/(X^2 - Y^2)

Now replace the X value from first equation

= [ (3Y/2)^2 + Y^2] / [ ((3Y/2)^2 - Y^2]

= [ (9Y^2/4) + Y^2] / [ (9Y^2/4) - Y^2]

= [ (9Y^2 + 4Y^2)/4] / [ (9Y^2 - 4Y^2)/4]

= (9Y^2 + 4Y^2) / (9Y^2 - 4Y^2)

= 13Y^2 / 5Y^2

= 13/5