simplify z-2/z-4 - z+1/z+4 + z-20/z^2-16

Answer 1

LCD = z^2-16 = (2-4)(z+4)

(z-2)/(z-4) - (z+1)/(z+4) +
(z-20)/z-4)(z+4) =
(z+4)(z-2/LCD-(z-4)(z+1)/LCD+(z-20)/LCD
= (z^2-2z+4z-8)/LCD-(z^2+z-4z-4)/LCD+
(z-20)/LCD
Combine like-terms in numerators:
(6z-24)/LD=6(z-4)/LCD=6(z-4)/(z-4)(z+4)