把下列分式化为部分分式~
问题描述：
把下列分式化为部分分式~
(1)5x-11/2x^2+x-6
(2)42-19x/(x^2+1)(x-4)
答
(1)[5x-11]/[2x^2+x-6]
=[5x-11]/[(2x-3)(x+2)]
=[5(x+2)-21]/[(2x-3)(x+2)]
=5(x+2)/[(2x-3)(x+2)-21/[(2x-3)(x+2)
=5/[2x-3]-21/[(2x-3)(x+2)]
(2)42-19x/(x^2+1)(x-4)
=[(72-19x)-30]/[(x^2+1)(x-4)]
=[-19(x-4)-30]/[x^2+1][x-4]
=-19/[x^2+1]-30/[x^2+1][x-4]