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:

$$x+4=0⟹x=-4$$

Thus, the rational expression is undefined at:

$$\boxed{{\displaystyle -4}}$$