1. **State the problem:** Simplify the expression $$\frac{7}{(d+3)(d-5)} \times \frac{d-5}{d+4}$$ as a single fraction in simplest form. 2. **Write the expression as a single fraction:** Multiply the numerators and denominators: $$\frac{7 \times (d-5)}{(d+3)(d-5) \times (d+4)}$$ 3. **Cancel common factors:** Notice that $(d-5)$ appears in both numerator and denominator, so we can cancel it: $$\frac{7 \times \cancel{(d-5)}}{(d+3) \times \cancel{(d-5)} \times (d+4)} = \frac{7}{(d+3)(d+4)}$$ 4. **Final simplified fraction:** $$\boxed{\frac{7}{(d+3)(d+4)}}$$ This is the simplest form because no further factors can be canceled.