#Ruby, 122 bytes

    require 'prime'
    ->n{x=Prime.take(n).map{|x|Rational(x)};f=x.shift;p x.reduce((f**2-1)/(f**2+1)){|x,y|x*(y**2-1)/(y**2+1)}}

Defines an anonymous function that takes a number and outputs the result to STDOUT as `(numerator/denominator)`.