化简分式:2a2+3a+2a+1−a2−a−5a+2−3a2−4a−5a−2+2a2−8a+5a−3.

问题描述:

化简分式:

2a2+3a+2
a+1
a2−a−5
a+2
3a2−4a−5
a−2
+
2a2−8a+5
a−3

2a2+3a+2
a+1
a2−a−5
a+2
3a2−4a−5
a−2
+
2a2−8a+5
a−3

=(2a+1)+
1
a+1
-(a-3)-
1
a+2
-(3a+2)+
1
a−2
+(2a-2)-
1
a−3

=[(2a+1)-(a-3)-(3a+2)+(2a-2)]+(
1
a+1
-
1
a+2
+
1
a−2
-
1
a−3

=
1
a+1
-
1
a+2
+
1
a−2
-
1
a−3

=
1
(a+1)(a+2)
-
1
(a−2)(a−3)

=
−8a+4
(a+1)(a+2)(a−2)(a−3)