# finding the limit of a function

#### coolbeans33

##### New member
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

##### Well-known member
MHB Math Helper
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 $$\displaystyle 2(z-3)$$. Since z never reaches 3 you can cancel $$\displaystyle x-3$$