计算(a+1/a2−a+4/1−a2)÷a2+2a−3a+3

问题描述:

计算(

a+1
a2−a
+
4
1−a2
a2+2a−3
a+3

原式=[

a+1
a(a−1)
+
4
(1−a)(1+a)
(a+3)(a−1)
(a+3)

=
(a+1)2−4a
a(a+1)(a−1)
÷(a-1)
=
(a−1)2
a(a+1)(a−1)
1
a−1

=
1
a2+a

故答案为
1
a2+a