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

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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 $$ \frac{9}{x-8} $$.
The simplified expression is $$ \frac{9}{x-8} $$.

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