Question

which shows all the values of a that make the rational expression \\(\frac{3a^2 - 27}{324 - 4a^2}\\) undefined?\
\\(\bigcirc\\) \\(a = 9\\)\
\\(\bigcirc\\) \\(a = 3\\)\
\\(\bigcirc\\) \\(a = -9\\) or \\(a = 9\\)\
\\(\bigcirc\\) \\(a = -3\\) or \\(a = 3\\)

Explanation:

Step1: Recall when rational expression is undefined

A rational expression \(\frac{f(a)}{g(a)}\) is undefined when the denominator \(g(a) = 0\). So we set the denominator \(324 - 4a^{2}=0\).

Step2: Solve the equation \(324 - 4a^{2}=0\)

First, we can rewrite the equation as \(4a^{2}=324\). Then divide both sides by 4: \(a^{2}=\frac{324}{4} = 81\). Taking the square root of both sides, we get \(a=\pm\sqrt{81}=\pm 9\).

Answer:

a = -9 or a = 9