如果整数A,B满足等式(A/X-1)-(B/X+2)=X+5/(X-1)(X+2),求A,B的值

问题描述:

如果整数A,B满足等式(A/X-1)-(B/X+2)=X+5/(X-1)(X+2),求A,B的值

通分
[A(X+2)-B(X-1)]/(X-1)(X+2)=(X+5)/(X-1)(X+2)
所以A(X+2)-B(X-1)=X+5
(A-B)X+(2A+B)=X+5
所以A-B=1 (1)
2A+B=5 (2)
(1)+(2)
3A=6
A=2
B=A-1=1