[tex] \frac{ {x}^{2} - 10x + 25 }{ {x}^{2} - 25 } \times \frac{x}{x - 5} + \frac{5}{x + 5} = \frac{ {x}^{2} + 2x( - 5) + {( - 5)}^{2} }{ {x}^{2} - {5}^{2} } \times \frac{x}{x - 5} + \frac{5}{x - 5} = \frac{ {(x - 5)}^{2} }{(x - 5)(x + 5)} \times \frac{x}{x - 5} + \frac{5}{x + 5} = \frac{ {(x - 5)}^{2 - 1} }{x + 5} \times \frac{x}{x - 5} + \frac{5}{x + 5} = \frac{x - 5}{x + 5} \times \frac{x}{x - 5} + \frac{5}{x + 5} = \frac{(x - 5)x}{(x + 5)(x - 5)} + \frac{5}{x + 5} = \frac{x}{x + 5} + \frac{5}{x + 5} = \frac{x + 5}{x + 5} = 1 [/tex]
