Question

若

4a-1

(a+2)(a-1)

=

m

a+2

+

n

a-1

，則（　�。�

• A、m=4，n=-4
• B、m=5，n=-1
• C、m=3，n=1
• D、m=4，n=1

Answer 1

分析：對(duì)等式右邊通分后進(jìn)行加減運(yùn)算，再根據(jù)對(duì)應(yīng)項(xiàng)系數(shù)相等列出方程組求解即可．

解答：解：若

4a-1

(a+2)(a-1)

=

m

a+2

+

n

a-1

=

m(a-1)+n(a+2)

(a+2)(a-1)

=

(m+n)a-(m-2n)

(a+2)(a-1)

∴

m+n=4 m-2n=1

解得m=3，n=1．
故選C．

點(diǎn)評(píng)：異分母分式加減運(yùn)算后利用對(duì)應(yīng)項(xiàng)系數(shù)相等求解是解本題的關(guān)鍵．