(x+2)/(x^2-4+4x)÷(x^2-4)/(x-2)

Question

identify the domain of the expression

 

Answer 1

Do you mean:

 

((x+2)/(x²-4+4x)) ÷ ((x²-4)/(x-2))

 

If so, then the domain is all real numbers EXCEPT for the values of x where:

 

1. The denominator of the dividend is 0 -- i.e., (x²-4+4x) = 0

2. The divisor is 0 -- i.e. (x²-4)/(x-2) = 0

3. The denominator of the divisor is 0 -- i.e., (x-2) = 0

 

These have to be excluded because they would each require some dividing by 0.

 

#1 is the case when (x²-4+4x) = 0.  Factor this into (x - 2)(x - 2) = 0.  The solution to this is x = 2.

#2 is the case when (x² - 4) = 0.  Factor this into (x - 2)(x + 2) = 0.  The solution to this is x = 2 or x = -2.

#3 is the case when x - 2 = 0.  The solution to this is x = 2.

 

So when x = 2 or -2, there expression is undefined, because it would require some dividing by 0.

 

Therefore the domain is all real numbers except for 2 and -2.