1. **State the problem:** Determine the values of $x$ for which the rational expression $$\frac{x^2 + 64}{8}$$ (a) equals zero and (b) is undefined. 2. **Recall the rules for rational expressions:** - A rational expression equals zero when its numerator equals zero. - A rational expression is undefined when its denominator equals zero. 3. **Analyze the numerator:** $$x^2 + 64 = 0$$ Solve for $x$: $$x^2 = -64$$ Since $x^2$ cannot be negative for real numbers, there are no real solutions. 4. **Analyze the denominator:** The denominator is 8, which is a constant and never zero. 5. **Conclusions:** - The expression never equals zero because the numerator $x^2 + 64$ is always positive. - The expression is never undefined because the denominator 8 is never zero. **Final answers:** - The expression never equals zero. - The expression is never undefined.