Question

計算

1

2x2+3x-1

-

2

2x2+3x+1

+

1

2x2+3x+3

．

Answer 1

分析：設2x²+3x=y，原式可變形為

1

y-1

-

2

y+1

+

1

y+3

，再通分化簡計算即可．

解答：解：設2x²+3x=y，則
原式=

1

y-1

-

2

y+1

+

1

y+3

=

(y+1)(y+3)-2(y-1)(y+3)+(y-1)(y+1)

(y-1)(y+1)(y+3)

=

8

(y-1)(y+1)(y+3)

=

8

(2x2+3x-1)(2x2+3x+1)(2x2+3x+3)

．

點評：此題主要考查了分式的加減運算，關鍵是掌握換元法的應用．