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

1 answer

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:

\[ \boxed{-4} \]