Answer:
-1
Step-by-step explanation:
|x-4|=x-4 when x-4 is positive or zero.
|x-4|=-(x-4) when x-4 is negative or zero.
x-4 is positive or zero means:
x-4>=0
Add 4 on both sides gives:
x>=4
x-4 is negative or zero means:
x-4<=0
Add 4 on both sides gives:
x<=4
Now we are approaching values of 4 from the left which means these values are less than 4 which makes x-4 negative.
So we are using:
|x-4|=-(x-4) when x-4 is negative or zero.
As x approaches 4 from left we have:
|x-4|/(x-4)=-(x-4)/(x-4)=-1.
