4x+1/x^2-7x+10=A/X-2 +B/x-5 求A ,B的值
问题描述：
4x+1/x^2-7x+10=A/X-2 +B/x-5 求A ,B的值
答
(4x+1)/(x²-7x+10)
=(4x+1)/(x²-7x+10)
=(4x+1)/([(x-2)(x-5)]
A/(X-2) +B/(x-5)
=[A(x-5)+B(x-2)]/[(x-2)(x-5)]
=[(A+B)x+(-5A-2B)]/[(X-2)(X-5)]
对照上述两式得
A+B=4,-5A-2B=1
A=-3,B=7