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
答
−2a2+3a+2 a+1
−
a2−a−5 a+2
+3a2−4a−5 a−2
2a2−8a+5 a−3
=(2a+1)+
-(a-3)-1 a+1
-(3a+2)+1 a+2
+(2a-2)-1 a−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)