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lim (x⁷-2x⁵+1)/(x³-3x²+2)x-1

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$\lim_{x \to 1} \frac{x^{7} - 2 x^{5} + 1}{x^{3} - 3 x^{2} + 2} = \lim_{x \to 1} \frac{x^{7} - x^{5} - x^{5} + 1}{x^{3} - x^{2} - 2 x^{2} + 2} \lim_{x \to 1} \frac{x^{5} (x^{2} - 1) - 1 (x^{5} - 1)}{x^{2} (x - 1) - 2 (x^{2} - 1)} \lim_{x \to 1} \frac{(x - 1) (x^{5} (x + 1) - x^{4} - x^{3} - x^{2} - x - 1)}{(x - 1) (x^{2} - 2 (x + 1))} \lim_{x \to 1} \frac{(x^{5} (x + 1) - x^{4} - x^{3} - x^{2} - x - 1)}{(x^{2} - 2 (x + 1))} = \frac{1 + 1 - 1 - 1 - 1 - 1 - 1}{1 - 2 - 2} = 1$

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