Question 819165
z-1/z^2+2z-8 , 2z+2/z^2-3z+2

z^2+2z-8

z^2+4z-2z-8
z(z+4)-2(z+4)

(z+4)(z-2)

z^2-3z+2

z^2-2z-z+2

z(z-2)-1(z-2)
(z-2)(z-1)

The LCD will be HCF * non common factors

HCF = (z-2)

LCD = (z-2)(z-1)(z+4)