Add and simplify: \( \frac{8}{x+8}+\frac{x+136}{x^{2}-64} \) \( \square \)

Calculate or simplify the expression \( \frac{8}{x+8}+\frac{x+136}{x^{2}-64} \). Simplify the expression by following steps: - step0: Solution: \(\frac{8}{x+8}+\frac{x+136}{x^{2}-64}\) - step1: Factor the expression: \(\frac{8}{x+8}+\frac{x+136}{\left(x-8\right)\left(x+8\right)}\) - step2: Reduce fractions to a common denominator: \(\frac{8\left(x-8\right)}{\left(x+8\right)\left(x-8\right)}+\frac{x+136}{\left(x-8\right)\left(x+8\right)}\) - step3: Rewrite the expression: \(\frac{8\left(x-8\right)}{\left(x-8\right)\left(x+8\right)}+\frac{x+136}{\left(x-8\right)\left(x+8\right)}\) - step4: Transform the expression: \(\frac{8\left(x-8\right)+x+136}{\left(x-8\right)\left(x+8\right)}\) - step5: Multiply the terms: \(\frac{8x-64+x+136}{\left(x-8\right)\left(x+8\right)}\) - step6: Calculate: \(\frac{9x+72}{\left(x-8\right)\left(x+8\right)}\) - step7: Factor the expression: \(\frac{9\left(x+8\right)}{\left(x-8\right)\left(x+8\right)}\) - step8: Reduce the fraction: \(\frac{9}{x-8}\) The simplified expression is \( \frac{9}{x-8} \).