题目内容
先化简，再求值：（
-
）+
，其中x=-1．
| x+2 |
| x2-2x |
| x-1 |
| x2-4x+4 |
| x-4 |
| x |
分析：先根据分式混合运算的法则把原式进行化简，再把x的值代入进行计算即可．
解答：解：原式=[
-
]+
=[
-
]+
=
+
=
+
=
=
，
当x=-1时，原式=
=
．
| x+2 |
| x(x-2) |
| x-1 |
| (x-2)2 |
| x-4 |
| x |
=[
| x2-4 |
| x(x-2)2 |
| x2-x |
| x(x-2)2 |
| x-4 |
| x |
=
| x2-4-x2+x |
| x(x-2)2 |
| x-4 |
| x |
=
| x-4 |
| x(x-2)2 |
| x-4 |
| x |
=
| (x-4)(x-2)2 |
| x(x-2)2 |
=
| x3+20x-16 |
| x(x-2)2 |
当x=-1时，原式=
| -1-20-16 |
| -1×(-1-2)2 |
| 37 |
| 9 |
点评：本题考查的是分式的混合运算，熟知分式混合运算的法则是解答此题的关键．
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