Question

化简：a³-a²-a+1/a³-3a²+3a-1

Answer 1

(a³-a²-a+1)/(a³-3a²+3a-1)
=(a-1)(a²-1)/(a-1)³
=(a-1)(a-1)(a+1)/(a-1)³
=(a+1)/(a-1)

希望对您有所帮助
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Answer 2

(a³-a²-a+1)/(a³-3a²+3a-1)
=[(a³-a)-(a²-1)]/[a³-1-3(a²-a)]
=[a(a²-1)-(a+1)(a-1)]/[(a³-1)-3(a²-a)]
=(a²-1)(a-1)/(a-1)(a²+a+1-3a)
=(a-1)²(a+1)/(a-1)³
=(a+1)/(a-1)

其实a³-3a²+3a-1=(a-1)³
还有：a³+3a²+3a+1=(a+1)³
这是立方公式！

类似a²-2a+1=(a-1)²
记住了，对以后解题也有帮助
希望能帮到你~

Answer 3

原式=[a²(a-1)-(a-1)]/[(a³-a²)-(2a²-3a+1)]
=(a-1)(a²-1)/[a²(a-1)-(2a-1)(a-1)]
=(a-1)²(a+1)/[(a-1)(a²-2a+1)
=(a-1)²(a+1)/(a-1)³
=(a+1)/(a-1)