Question

Does there exist a fraction(s) m/n for which it is true that m/n= (m+b)/(n+b) ? If so, for which fraction(s). If not, explain why. Remember, if you say that such a fraction does exist, simply offering one example will not suffice as a full justification.

Answer 1

m/n= (m+b)/(n+b)

m(n+b) = n(m+b)
mn+mb = mn+nb
b(m-n)=0
b=0 or m=n

The question is poorly explained. It clearly said

Does there exist a fraction(s) m/n...

so offering a single example would indeed answer the question!