1. **State the problem:** Rearrange the equation $$\left(a + \frac{b}{c}\right)(d - e) = f$$ to isolate the variable $a$. 2. **Formula and rules:** To isolate $a$, we need to undo the multiplication by $(d - e)$ by dividing both sides by $(d - e)$, assuming $d \neq e$ to avoid division by zero. 3. **Divide both sides by $(d - e)$:** $$a + \frac{b}{c} = \frac{f}{d - e}$$ 4. **Isolate $a$ by subtracting $\frac{b}{c}$ from both sides:** $$a = \frac{f}{d - e} - \frac{b}{c}$$ 5. **Final answer:** $$a = \frac{f}{d - e} - \frac{b}{c}$$ This expression shows $a$ isolated in terms of $b$, $c$, $d$, $e$, and $f$.