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= {(A -2) × (A² + 2A - 3) + (A² - 5A) × (A -1)} / (A -1) × (A² + 2A - 3)
= (A³ + 2A² - 3A - 2A² - 4A + 6) + (A³ - A² - 5A² + 5A) / (A³ + 2A² - 3A - A² - 2A +3)
= (A³ - 7A + 6) + (A³ - 6A² + 5A) / (A³ + A² - 5A + 3)
= 2A³ - 6A² - 2A + 6 / A³ + A² - 5A + 3
A³ + A² - 5A + 3 = 2A³ - 6A² - 2A + 6
= (2A³ - A³) - (6A² -A²) - (2A + 5A) + (6 - 3)
= A³ - 7A² + 3A + 3