1. The problem is to simplify and solve the expression $\left(a + \frac{b}{c}\right)(d - e) = f$ for $a$. 2. Start by expanding the left side using the distributive property: $$\left(a + \frac{b}{c}\right)(d - e) = a(d - e) + \frac{b}{c}(d - e)$$ 3. This expands to: $$a(d - e) + \frac{b(d - e)}{c} = f$$ 4. To isolate $a$, subtract $\frac{b(d - e)}{c}$ from both sides: $$a(d - e) = f - \frac{b(d - e)}{c}$$ 5. Now divide both sides by $(d - e)$ to solve for $a$: $$a = \frac{f - \frac{b(d - e)}{c}}{d - e}$$ 6. Simplify the complex fraction by multiplying numerator and denominator appropriately: $$a = \frac{f - \frac{b(d - e)}{c}}{d - e} = \frac{f - \frac{b(d - e)}{c}}{d - e} \times \frac{c}{c} = \frac{cf - b(d - e)}{c(d - e)}$$ 7. The final expression for $a$ is: $$a = \frac{cf - b(d - e)}{c(d - e)}$$ This formula allows you to find $a$ given values for $b$, $c$, $d$, $e$, and $f$.