algebra 1 help please?

Question

 

z^2-3z+2            z^2+6z+8

                    .        

z^2+3z-4               z^2-4

Answer 1

z² - 3z + 2       z² - 6z + 8

------------  *   -------------   =

z² +3z - 4          z² - 4

 

(z-2)(z-1)         (z+4)(z+2)

-----------   *   ---------------   =

(z+4)(z-1)       (z-2)(z+2)

 

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

------------------------  = 1

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

 

All elements of the numerator cancel with

elements of the denominator.  The answer is 1

 

Answer 2

(z² - 3z + 2)(z² + 6z + 8) / (z² + 3z - 4)(z² - 4)

 

= (z-1)(z-2)(z+2)(z+4) / (z+3)(z-1)(z+2)(z-2)

 

= (z+4) / (z+3)