等式两边同时乘以(X^2-4),得:
A(X^2-4)/(X-2)+B(X^2-4)/(X+2)=1
而(X^2-4)=(X+2)*(X-2),所以
上式化简得:
A(X+2)+B(X-2)=1
(A+B)X+2(A-B)=1
所以有:
A+B=0
A-B=1/2
解得:A=1/4;
B=-1/4
等式两边同时乘以(X^2-4),得:
A(X^2-4)/(X-2)+B(X^2-4)/(X+2)=1
而(X^2-4)=(X+2)*(X-2),所以
上式化简得:
A(X+2)+B(X-2)=1
(A+B)X+2(A-B)=1
所以有:
A+B=0
A-B=1/2
解得:A=1/4;
B=-1/4