The other day, I was solving problems regarding rational expressions. I noticed that every single time, after simplifying the numerator, the fraction is already in lowest terms. So I wondered if this is always true.
After a bit of experimentation, I was able to construct this counterexample:
Can you think of a way to generate infinitely-many such problems?
Here are some assumptions:
All the coefficients are integers.
The addends are already in lowest terms.
After simplifying the numerator, the numerator and the denominator stilll has a common factor.