1、
6/(x-1)=(1+k)/(x-1)-3/x
3/x=(1+k-6)/(x-1)=(k-5)/(x-1)
3x-3=(k-5)x
(k-5-3)x=-3
x=-3/(k-8)
k≠8
2、
x+1/x=5
(x+1/x)^2=25
x^2+1/x^2+2=25
x^2+1/x^2=25-2=23
3、
(4x+1) / (x^2-7x+10)=A/(x-2)+B/(x-5)
(4x+1) / [(x-2)(x-5)]=[A(x-5)+B(x-2)] / [(x-2)(x-5)]
4x+1=(A+B)x+(-5A-2B)
A+B=4,-5A-2B=1
A=-3,B=7