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= [ (1/p + 1/q)(1/p - 1/q) ÷ (p - q)(p + q) ] * (pq)²
= [ (1/p)² - (1/q)² ÷ (p² - q)² ] * (pq)²
= [ 1/p² - 1/q² ÷ (p² - q²) ] * (pq)²
= [{(q² - p²)/p²q²} ÷ (p² - q²)] * p²q²
= [ -(p² - q²)/p²q² × 1/(p² - q²) ] * p²q²
= [ -1 / p²q² ] * p²q²
= -p²q² / p²q²
= -1
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