Question

What value would cause the rational expression to be undefined?
(2x+12)/(-2x^2 -16x-32)
1)x=-4
2)x=-6
3)x=6
4)x=4

Answer 1

To determine the value(s) that would cause the rational expression \((2x + 12)/(-2x^2 - 16x - 32)\) to be undefined, we need to find the values of \(x\) that make the denominator equal to zero.

The denominator is given by:

\[
-2x^2 - 16x - 32
\]

First, we set the denominator equal to zero:

\[
-2x^2 - 16x - 32 = 0
\]

To make the equation simpler, we can factor out \(-2\):

\[
-2(x^2 + 8x + 16) = 0
\]

Now we can focus on the quadratic part:

\[
x^2 + 8x + 16 = 0
\]

Next, we can factor the quadratic:

\[
(x + 4)(x + 4) = 0 \quad \text{or} \quad (x + 4)^2 = 0
\]

This gives us:

\[
x + 4 = 0 \quad \Rightarrow \quad x = -4
\]

Thus, the value that causes the rational expression to be undefined is \(x = -4\).

Now, reviewing the provided options:
1. \(x = -4\) (Undefined)
2. \(x = -6\) (Not undefined)
3. \(x = 6\) (Not undefined)
4. \(x = 4\) (Not undefined)

The correct answer is:

**1) \(x = -4\)**.