代數分式問題數條

1.
(3ax - ay - 3x + y) / (3x - y)
= [(3ax- ay) - (3x - y)] / (3x - y)
= [a(3x- y) - (3x - y)] / (3x - y)
= (a - 1)(3x - y) / (3x - y)
= a -1


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2.
(2a + 2b) / (3b + 3a)²
= (2a + 2b) /(3a + 3b)²
= 2(a + b) / [3(a + b)]²
= 2(a + b) / 9(a + b)²
= 2 /9(a + b)


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3.
[(m - 5) / n³] × [4n / (3m - 15)]
= [(m - 5) / n³] × [4n/ 3(m - 5)]
= 4n(m - 5) / 3n³(m - 5)
= 4 / 3n²


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4.
[(x - x²) /12x³] ÷ [(5x - 5) /6x]
= [(x - x²) /12x³] • [6x / (5x - 5)]
= [x(1 - x) / 12x³] • [6x/ 5(x - 1)]
= [-x(x - 1) / 12x³] • [6x/ 5(x - 1)]
= -6x²(x - 1) / 60x³(x - 1)
= -10 / x