Question

Доказать тождество
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Answer 1

Сводим к общему знаменателю:


$\frac{x^{2} + 1}{(x - 3)^{2}} - \frac{5x}{(x - 3)^{2}} + \frac{8 - x}{(x - 3)^{2}} = \frac{x^{2} + 1 - 5x + 8 - x}{(x - 3)^{2}} = \frac{x^{2} -6x + 9}{(x - 3)^{2}} = \frac{(x - 3)^{2}}{(x - 3)^{2}} = 1$