Subtract and simplify. \( \frac{8}{x-9}-\frac{11}{x+9} \) \( \begin{array}{l}\frac{171}{x-9} \\ \frac{\frac{-3 x+171}{x^{2}-81}}{x^{2}-81} \\ \frac{-3 x-171}{x^{2}-81} \\ x^{2}-81\end{array} \)

To subtract the fractions \( \frac{8}{x-9} - \frac{11}{x+9} \), we first need a common denominator, which is \( (x-9)(x+9) \) or \( x^2 - 81 \). Now, rewrite the fractions: \[ \frac{8(x+9)}{(x-9)(x+9)} - \frac{11(x-9)}{(x-9)(x+9)} \] This becomes: \[ \frac{8(x+9) - 11(x-9)}{x^2 - 81} \] Expanding the numerators gives: \[ 8x + 72 - 11x + 99 = -3x + 171 \] So, we have: \[ \frac{-3x + 171}{x^2 - 81} \] Thus, the final simplified form is: \[ \frac{-3x + 171}{x^2 - 81} \]