Question

what value would cause the rational expression 5x+15/−2x^2−16x−32 to be undefined?

Answer 1

A rational expression is undefined when its denominator is equal to zero. In this case, the rational expression is given by:

\[
\frac{5x + 15}{-2x^2 - 16x - 32}
\]

To find the values of \( x \) that make this expression undefined, we need to set the denominator equal to zero and solve for \( x \):

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

Let's simplify by dividing the entire equation by -2:

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

Next, we can factor the quadratic equation:

\[
(x + 4)(x + 4) = 0
\]

or, equivalently,

\[
(x + 4)^2 = 0
\]

Setting the factor equal to zero gives:

\[
x + 4 = 0 \implies x = -4
\]

Thus, the rational expression is undefined at:

\[
\boxed{-4}
\]