1.已知2x-3/(x-1)(x+2)=A/x-1+B/x+2，则A=B=2.计算：2/(x+1)(x+3)+2/(x+3)(x+5)…+2/(x+1997)(x+1999)一小题我得后一步是A(x+2)+B(x-1)=2x-3，但是解不出来呢？做第二题这种类型的题应该怎么着手呢？

Question

1.已知2x-3/(x-1)(x+2)=A/x-1+B/x+2，则A= B=
2.计算：2/(x+1)(x+3)+2/(x+3)(x+5)…+2/(x+1997)(x+1999)
一小题我得后一步是A(x+2)+B(x-1)=2x-3，但是解不出来呢？
做第二题这种类型的题应该怎么着手呢？

Answer 1

1、A/x-1+B/x+2
=【A(x+2)+B(x-1)】/(x-1)(x+2)=2x-3)/(x-1)(x-2)
A(x+2)+B(x-1)=2x-3
Ax+2A+Bx-B=2x-3
x(A+B)+(2A-B)=2x-3
A+B=2
2A-B=-3
A=-1/3
B=7/3
2、2/(x+1)(x+3)+2/(x+3)(x+5)…+2/(x+1997)(x+1999)
=1/(x+1)-1/(x+3)+1/(x+3)-1/(x+5)+.+1(x+1997)-1/(x+1999)
=1/(x+1)-1/(x+1999)
=1998/(x+1)(x+1999)