Докажите тождество ((x^2-10x+25)/(x^2-25))^3:((x-5)/(x+5))^3=1.

\[\left( \frac{x^{2} - 10x + 25}{x^{2} - 25} \right)^{3}\ :\left( \frac{x - 5}{x + 5} \right)^{3} = 1\]

\[\left( \frac{(x - 5)^{2}}{(x - 5)(x + 5)} \right)^{3} \cdot \frac{(x + 5)^{3}}{(x - 5)^{3}} = 1\]

\[\frac{(x - 5)^{3} \cdot (x + 5)^{3}}{(x + 5)^{3} \cdot (x - 5)^{3}} = 1\]

\[1 = 1 \Longrightarrow ч.т.д.\]