Question

如果(2x+3)/(x-2)^2=a/(x-2)+b/(x-2)^2,求常数ab的值

Answer 1

(2x+3)/(x-2)^2=a/(x-2)+b/(x-2)^2

(2x+3)/(x-2)^2=a(x-2)/(x-2)^2+b/(x-2)^2

则有2x+3= a(x-2)+b

2x+3= ax-2a+b

令a=2

-2a+b= 3

得a=2,b=7

a*b=14