Упростите выражение:
а)

\frac{x^{2}}{(x - 5)^{2}} - \frac{25}{(5 - x)^{2}}

;
б)

\frac{x^{2} + 25}{(x - 5)^{3}} + \frac{10 x}{(5 - x)^{3}}

Упростите выражение: а) x 2 ( x − 5 ) 2 − 25 ( 5 − x ) 2 ; б) x 2 + 25 ( x − 5 ) 3 + 10 x ( 5 − x ) 3 .

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

\frac{x^{2} + 25}{(x - 5)^{3}} + \frac{10 x}{(5 - x)^{3}} = \frac{x^{2} + 25}{(x - 5)^{3}} - \frac{10 x}{(x - 5)^{3}} = \frac{x^{2} - 10 x + 25}{(x - 5)^{3}} = \frac{(x - 5)^{2}}{(x - 5)^{3}} = \frac{1}{x - 5}