Question

(1)解方程:1-x2-x-3=1x-2; (2)计算0.25×(-2)-2÷(...

(1)解方程:1-x2-x-3=1x-2; (2)计算0.25×(-2)-2÷(16)-1-(π-3)0; (3)先化简(x+1x-1+1x2-2x+1)÷xx-1,然后选取一个你喜欢的x的值代入计算.

Answer 1

(1)方程两边同乘(x-2),
得:x-1-3(x-2)=1,
整理解得x=2.
经检验,x=2是原方程的增根,
故原方程无解.
(2)原式=0.25×
1
4
×16-1=1-1=0.
(3)(
x+1
x-1
+
1
x2-2x+1
)÷
x
x-1
=[
x+1
x-1
+
1
(x-1)2
]•
x-1
x
=
x+1
x
+
1
x(x-1)
=
x2-1
x(x-1)
+
1
x(x-1)
=
x
x-1
,
取x=2,得原式=2.