Question

问一道初二分式计算题?如(1+3x)/(x^2-1)=a/(x+1)+b(x-1),求a,b的值?请写出答题具体过程并求

Answer 1

a/(x+1)+b(x-1)

=[a(x-1)+b(x+1)]/(x+1)(x-1)

=[(a+b)x+(b-a)]/(x^2-1)

=(1-3x)/(x^2-1)

所以(a+b)x+(b-a)=-3x+1

所以a+b=-3,b-a=1

相加

2b=-2

b=-1,a=-3-b=-2