51. 解：原式

．

50. 解：

49. 解：原式＝

　　＝

　　＝

当x＝5时，原式＝

48. 解：原式

．

当时，原式

47. 解：原式=

==

=

当时，原式=

46. 解:当时,

原式

45. 解：设改进操作方法后每天生产件产品，则改进前每天生产件产品．

依题意有．

整理得．

解得或． 时，，舍去．

．

答：改进操作方法后每天生产60件产品．

44. ．解：原式

　　　　　　 ········································································ (2分)

　　　　　 ．··························································································· (4分)

当，时，

原式．··················································································· (6分)

43.

解：方程两边同乘(x-1)(x+1),得

　　　　　 2(x-1)-x=0. ………………………………………………………3分

解这个方程，得

　　　 x=2. …………………………………………………………………5分

检验：当x=2时，(x-1)(x+1)≠0.

所以x=2是原方程的解. …………………………………………………6分

42. 解：原式＝　

＝+1

＝．　

当x＝时，原式＝＝－4．