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Решите задачу:

$\left(x+5-\frac{50}{5-x}\right):\frac{x^2+25}{x^2-10x+25}\cdot\frac{1}{x+5}=$

$\left(x+5+\frac{50}{x-5}\right):\frac{x^2+25}{(x-5)^2}\cdot\frac{1}{x+5}=$

$\left( \frac{(x+5)(x-5)}{x-5} +\frac{50}{x-5}\right) \cdot \frac{(x-5)^2}{x^2+25}\cdot\frac{1}{x+5}=$

$\left( \frac{x^2-25 +50}{x-5}\right) \cdot \frac{(x-5)^2}{(x^2+25)(x+5)}=$

$\frac{x^2 +25}{x-5}\cdot \frac{(x-5)^2}{(x^2+25)(x+5)}=$

$\frac{x-5}{x+5}$