In fact denominators are often unpleasant to work with in general (especially if they can vanish or at least become small), which is why it is often a good idea to clear denominators (though this can be a tradeoff, as it can make the resulting expressions far longer, if there are many different denominators that need to be cleared).
One particular trick for eliminating denominators that is perhaps not as well known is to apply the fundamental theorem of calculus: for a differentiable function 𝑓, the Newton quotient ( \frac{f(x+h)-f(x)}{h} ) can be rewritten as ( \int_0^1 f'(x+th)\ dt ). Another way of thinking about this is: in expressions with a small denominator h, one now gains the freedom to modify any term 𝑓(𝑥) in the numerator with a perturbed term 𝑓(𝑥+h) (or more generally 𝑓(𝑥+𝑎h) for some 𝑎), at the cost of introducing some auxiliary expression such as ( \int_0^1 f'(x+th)\ dt ) that has no denominator and is thus presumably easier to work with. (2/3)