Question

I didn’t understand how to do this nor explain it correctly, please help,

Answer 1

-2

Explanation:

We have the following expression:

`\mleft((x^2-4)/(x^2+4x+4)\mright)\mleft(x^2-x-6\mright)`

In this case, the only way that the function becomes discontinuous is when the denominator is equal to 0, that is, we must equal the denominator to 0 and in this way we will be able to know the value that x cannot take.

`\begin{gathered} x^2+4x+4=0 \\ x^2+4x+4=(x+2)^2 \\ (x+2)^2=0 \\ x+2=0 \\ x=-2 \end{gathered}`

Therefore, x cannot have a value of -2, since if it takes this value, the denominator is 0 and the division by 0 is not defined.