若a/(x-2)+b/(x+1)=3x(x-2)(x+1),且a、b都是常数,则a=b=若a/(x-2)+b/(x+1)=3x(x-2)(x+1),且a、b都是常数,则a=b=

Question

若a/(x-2)+b/(x+1)=3x(x-2)(x+1),且a、b都是常数,则a= b=
若a/(x-2)+b/(x+1)=3x(x-2)(x+1),且a、b都是常数,则a= b=

Answer 1

a/(x-2)+b/(x+1)
=[a(x+1)+b(x-2)]/(x-2)(x+1)
=[(a+b)x+a-2b]/(x-2)(x+1)
=3x/(x-2)(x+1)
对比,得
a+b=3
a-2b=0
解得
a=2 b=1