Adding fractions of unlike denominators

Question

Given $\frac{1}{s}+\frac{1}{r} = ?$ , can I simplify the equation by multiplying the equation with $rs$?

and the equation is simplified as $rs * (\frac{1}{s}+\frac{1}{r}) = r + s$

Is this a valid operation?

Answer 1

Just $$\frac{1}{s}+\frac{1}{r}=\frac{r+s}{rs}.$$ If $$\frac{1}{s}+\frac{1}{r}=t$$ so $$r+s=trs$$

But $$r+s\neq\frac{1}{s}+\frac{1}{r},$$ of course.