*If I turn out to have a wrong answer, please no hints or showing an valid proof. I want to do it on my own ! ad/bd-bc/bd=+-1/bd is neighbor fraction Now, reduce the common numbers : a/b-c/d=+-1/bd We must now prove that the left hand side has irreductible fractions. Lets see what would happen if these fraction were reductible. let a=z*y , b=z*l , c=p*m d=p*n z*y/z*l-p*m/p*n equality to be determined +-1/(z*l)*(p*n) Reduce: *ln (y/l-m/n) equality to be determined (+-1/(z*l)*(p*n))*ln yn-lm equality to be determined +-1/z*p yn-lm not= +-1/z*p We have considered the initial fractions to be reductible and have arrived at a false result. An integer cannot be equal to (+-1/z*p) So, the initial fractions must be irreductible. *Of course, I'm considering the variables to represents integers.