a,b取什么值时,分式(3x-4)/(x-3x+2)=a/(x-1)+b/(x-2)是恒等式?

问题描述:

a,b取什么值时,分式(3x-4)/(x-3x+2)=a/(x-1)+b/(x-2)是恒等式?

两边同乘以x² - 3x + 2得
3x - 4 = a(x - 2)+ b(x - 1)
= (a + b)x - 2a - b
所以a + b = 3,2a + b = 4
解得a = 1,b = 2