Question

計(jì)算化簡(jiǎn)：

x

x2+3x+2

+

x

x2+x-2

+

2

1-x2

．

Answer 1

分析：首先把各分式分母分解因式，再通分，然后進(jìn)行分式的加減運(yùn)算．

解答：解：原式=

x

(x+2)(x+1)

+

x

(x+2)(x-1)

+

2

(1+x)(1-x)

=

x(x-1)

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

+

x(x+1)

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

-

2(x+2)

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

=

x2-x +x2+x-2x-4

(x+2)(x2-1)

=

2x2-2x-4

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

=

2(x-2)(x+1)

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

=

2x-4

x2+x-2

．

點(diǎn)評(píng)：此題考查的知識(shí)點(diǎn)是粉飾的加減法，關(guān)鍵如果是同分母分式，那么分母不變，把分子直接相加減即可；如果是異分母分式，則必須先通分，把異分母分式化為同分母分式，然后再相加減．