问题 解答题
计算:
x-3
x2-1
-
3
1-x
=
x-3
(x+1)(x-1)
-
3
x-1
…(A)
=
x-3
(x+1)(x-1)
-
3(x+1)
(x+1)(x-1)
…(B)
=x-3-3(x+1)…(C)
=-2x-6…(D)
(1)在上述计算过程中,从______开始出现错误;
(2)从B到C______(填“正确”或“不正确”),若不正确,错误的原因是______.
正确答案是______.
答案

(1)

x-3
x2-1
-
3
1-x
=
x-3
(x+1)(x-1)
+
3
x-1

故从(A)开始出现错误;

(2)从(B)到(C)不正确,错误的原因是:没有正确运用同分母分式相加减的运算法则.

正确答案是:

x-3
x2-1
-
3
1-x
=
x-3
(x+1)(x-1)
+
3
x-1

=

x-3
(x+1)(x-1)
+
3(x+1)
(x+1)(x-1)

=

x-3+3x+3
(x+1)(x-1)

=

4x
(x+1)(x-1)

故答案为

4x
(x+1)(x-1)

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