$\frac{1}{\infty-\infty}$ is an indeterminate form? I know that $$\infty-\infty$$is an indeterminate form .. What about $$\frac{1}{\infty-\infty}$$ is it an indeterminate form or is it equal to zero ?

It is easy to construct examples where the limit is $0$ such as

$$\lim_{x\to\infty}\frac{1}{x^2-x}=0$$

But other examples can be constructed such as

$$\lim_{x\to\infty}\frac{1}{(x+a)-x}=\frac{1}{a}$$

So it is an indeterminate form.