Question

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

Answer 1

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