Solve For S 4Af92F

1. **State the problem:** Solve for $s$ in the equation $$\frac{s + 6}{s + 9} = \frac{s + 3}{s + 5}.$$ 2. **Use the cross-multiplication formula:** For two fractions equal to each other, $$\frac{a}{b} = \frac{c}{d}$$ implies $$a \times d = b \times c.$$ 3. **Apply cross multiplication:** $$ (s + 6)(s + 5) = (s + 9)(s + 3) $$ 4. **Expand both sides:** $$ s^2 + 5s + 6s + 30 = s^2 + 3s + 9s + 27 $$ $$ s^2 + 11s + 30 = s^2 + 12s + 27 $$ 5. **Simplify by subtracting $s^2$ from both sides:** $$ \cancel{s^2} + 11s + 30 = \cancel{s^2} + 12s + 27 $$ $$ 11s + 30 = 12s + 27 $$ 6. **Isolate $s$ terms:** Subtract $11s$ from both sides: $$ 11s + 30 - 11s = 12s + 27 - 11s $$ $$ 30 = s + 27 $$ 7. **Solve for $s$:** Subtract 27 from both sides: $$ 30 - 27 = s + 27 - 27 $$ $$ 3 = s $$ 8. **Check for restrictions:** Denominators cannot be zero: $s + 9 \neq 0 \Rightarrow s \neq -9$ $s + 5 \neq 0 \Rightarrow s \neq -5$ 9. **Final answer:** $$ s = 3 $$