Question

Which domain restrictions apply to the rational expression? x^2+4x+4 / x^2−4 Select each correct answer x≠−4 x≠−2 x≠0 x≠2 x≠4

Answer 1

The correct answers are x≠2 and x≠(-2).

Domain restrictions are any points in the domain where the function will not have a value.  This basically means that it's a point where x won't work in the function.

For the numerator, any value will work for x.  We can have a value of 0 in the numerator, or a positive, negative, or decimal number.

However, the denominator cannot equal 0.  This is because a fraction bar represents division, and we cannot divide by 0.  The values that make the denominator 0 can be found by:

x²-4=0

Add 4 to both sides:
x²-4+4 = 0+4
x² = 4

Take the square root of both sides:
√x² = √4

x = 2 or x = -2.

Answer 2

Answer:

The restrictions on domain are are: $x \neq -2, x\neq 2$  

Step-by-step explanation:

We are given the following information in the question:

We are given an expression:

$\displaystyle\frac{x^2 + 4x +4}{x^2-4}$

Simplifying the given fraction, we have,

$\displaystyle\frac{x^2 + 4x +4}{x^2-4}\\\\=\frac{(x+2)^2}{(x+2)(x-2)}\\\\=\frac{(x+2)(x+2)}{(x+2)(x-2)}$

The domain is basically collection of all values of x such that the expression is defined.

We need to make sure that the denominator is not equal to zero for the given fraction.

Thus,

$(x+2)(x-2) \neq 0\\\Rightarrow (x+2) \neq 0, (x-2) \neq 0\\\Rightarrow x \neq -2, x\neq 2$

Hence, the restrictions on domain are are:

$x \neq -2, x\neq 2$