先化简,再求值:2/xy+x+3/x2−x÷x2y+2xy−3yx2−2x+1,其中x=2+3,y=2−3.

问题描述:

先化简,再求值:

2
xy
+
x+3
x2−x
÷
x2y+2xy−3y
x2−2x+1
,其中x=2+
3
,y=2−
3

原式=

2
xy
+
x+3
x(x−1)
÷
y(x2+2x−3)
(x−1)2

=
2
xy
+
x+3
x(x−1)
(x−1)2
y(x−1)(x+3)

=
3
xy

当x=2+
3
,y=2-
3
时,原式=
1
(2+
3
)(2−
3
)
=1.