Question

計算：(

x+3

x2-3x

-

x-1

x2-6x+9

)÷

x-9

x

．

Answer 1

分析：先把括號內的分式通分，然后再按照分式的混合運算法則計算．

解答：解：原式=[

x+3

x(x-3)

-

x-1

(x-3)2

]÷

x-9

x

=[

(x+3)(x-3)

x(x-3)2

-

x(x-1)

x(x-3)2

]÷

x-9

x

=

x2-9-x2+x

x(x-3)2

×

x

x-9

=

1

(x-3)2

．
故答案為

1

(x-3)2

．

點評：本題主要考查分式的混合運算，通分、因式分解和約分是解答的關鍵．