MHB How Do You Find the Limit of A(z) as z Approaches 3?

[coolbeans33]

A(z)= 2z-6/ z²-5z+6

find the limit as z-->3

I factored the denominator to get (z-2)(z-3), and manipulated the function to get:

2z²-6²/(z-2)(z-3)(2z+6)

but I'm just not sure what to do in order to get rid of the (z-3)

I hope there's some obvious answer that I'm not seeing!

 

[SuperSonic4]

A(z)= 2z-6/ z²-5z+6

find the limit as z-->3

I factored the denominator to get (z-2)(z-3), and manipulated the function to get:

2z²-6²/(z-2)(z-3)(2z+6)

but I'm just not sure what to do in order to get rid of the (z-3)

I hope there's some obvious answer that I'm not seeing!

You can factor the numerator to $$2(z-3)$$. Since z never reaches 3 you can cancel $$x-3$$