Question

分式的乘除计算:

(1)m/m²-1·m²+m/m²；
(2)x-2/3-x·x²-6x+9/x²-4；
(3)3x-6/x²-4÷x+2/x²+4x+4；
(4)x²-2x+1/x²-1÷x-1/x²+x.

Answer 1

(1)[m/(m²-1)](m²+m)/m²=m²/(m²-1)](m+1)/m²=1/(m-1)
(2)[(x-2)/(3-x)][(x²-6x+9)/(x²-4)]
=[(x-2)/(3-x)][(x-3)²)/(x+2)(x-2)]
=-[(x-2)(x-3)(x+3)]/[(x-3)(x+2)(x-2)]
=-(x+3)/(x-2)

(3)(3x-6)/(x²-4)÷(x+2)/(x²+4x+4)
=[3(x-2)/(x²-4)][(x+2)²/(x+2)]
={3(x-2)(x+2)²}/[(x-2)(x+2)²]
=3

(4)(x²-2x+1)/(x²-1)÷(x-1)/(x²+x.)
=[(x-1)²x(x+1)]/[(x+1)(x-1)²]
=x