Question

algebra: concepts and connections - plc investigating rational and irrational numbers which shows all the values of a that make the rational expression \\(\frac{3a^2 - 27}{324 - 4a^2}\\) undefined? options: \\(a = 9\\), \\(a = -3\\) or \\(a = 3\\), \\(a = -9\\) or \\(a = 9\\), \\(a = 3\\)

Explanation:

Step1: Set denominator equal to 0

$324 - 4a^2 = 0$

Step2: Rearrange to isolate $a^2$

$4a^2 = 324$

Step3: Solve for $a^2$

$a^2 = \frac{324}{4} = 81$

Step4: Find square roots of 81

$a = \sqrt{81}$ or $a = -\sqrt{81}$

Answer:

$a = -9$ or $a = 9$