问题 填空题
化简
1
a
+
1
b
(1+
1
a
)+
1
c
(1+
1
a
)(1+
1
b
)+
1
d
(1+
1
a
)(1+
1
b
)(1+
1
c
)-(1+
1
a
)(1+
1
b
)(1+
1
c
)(1+
1
d
)
的值为______.
答案

原式=

1
a
+
1
b
(1+
1
a
)+
1
c
(1+
1
a
)(1+
1
b
)+(1+
1
a
)(1+
1
b
)(1+
1
c
)(
1
d
-1-
1
d

=

1
a
+
1
b
(1+
1
a
)+
1
c
(1+
1
a
)(1+
1
b
)-(1+
1
a
)(1+
1
b
)(1+
1
c

=

1
a
+
1
b
(1+
1
a
)+(1+
1
a
)(1+
1
b
)(
1
c
-1-
1
c

=

1
a
+
1
b
(1+
1
a
)-(1+
1
a
)(1+
1
b

=

1
a
-(1+
1
a

=-1

故答案是:-1.

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