16) \( \frac{5}{r-9}=\frac{8}{r+5} \)

To solve the equation \( \frac{5}{r-9}=\frac{8}{r+5} \), you can cross-multiply to eliminate the fractions. This gives you: \[ 5(r + 5) = 8(r - 9) \] Expanding both sides results in: \[ 5r + 25 = 8r - 72 \] Now, rearranging it to isolate \( r \): \( 25 + 72 = 8r - 5r \) which simplifies to: \( 97 = 3r \) Finally, divide by 3: \( r = \frac{97}{3} \) So the answer is \( r \approx 32.33 \). Keep in mind that both sides of the original equation must also be defined, so \( r \neq 9 \) and \( r \neq -5\) to avoid division by zero.