Subtract and reduce to lowest terms if possible

Question

8 - 8

__ __

Z-1 1-Z

Answer 1

Hi Marie;

[8/(z-1)]-[8/(1-z)]

Let's multiply the first bracketed expression by (1-z)/(1-z)

Let's multiply the second bracketed expression by (z-1)/(z-1)

{[(8)(1-z)]/[(z-1)(1-z)]}  -  {[(8)(z-1)]/[(1-z)(z-1)]}

With both bracketed expressions having the same denominator, we can execute the subtraction of the numerator...

{[(8)(1-z)]-[(8)(z-1)]}/[(1-z)(z-1)]

(8-8z-8z+8)/[(1-z)(z-1)]

(16-16z)/[(1-z)(z-1)

[(16)(1-z)]/(1-z)(z-1)]

The parenthetical expression (1-z) is in the numerator and denominator.  It cancels...

[(16)(1-z)]/(1-z)(z-1)]

16/(z-1)

Answer 2

8/(z-1) - 8/(1-z)

 

= 8/(z-1) + 8/(z-1)

 

= 2*8/(z-1)

 

= 16/(z-1)