Question

先化簡，再求值：（

x+2

x2-2x

-

x-1

x2-4x+4

）÷

x-4

x3-2x2

，x=-2．

Answer 1

分析：先根據(jù)分式混合運(yùn)算的法則把原式進(jìn)行化簡，再把x的值代入進(jìn)行計算即可．

解答：解：原式=（

x+2

x(x-2)

-

x-1

(x-2)2

）÷

x-4

x2(x-2)

=

(x+2)(x-2)-x(x-1)

x(x-2)2

×

x2(x-2)

x-4

=

x2-4-x2+x

x(x-2)2

×

x2(x-2)

x-4

=

x-4

x(x-2)2

×

x2(x-2)

x-4

=

x

x-2

，
當(dāng)x=-2時，原式=

-2

-2-1

=

2

3

．

點(diǎn)評：本題考查的是分式的化簡求值，熟知分式混合運(yùn)算的法則是解答此題的關(guān)鍵．