Question

which value(s) of x will be excluded from the domain of the rational function? y = \frac{3x - 1}{x^{2}-9}
-3
3
-3, 3
\frac{1}{3}

Explanation:

Step1: Recall domain - exclusion rule

The domain of a rational function excludes values that make the denominator zero. So we set the denominator $x^{2}-9 = 0$.

Step2: Factor the denominator

We know that $x^{2}-9=(x + 3)(x - 3)$ (using the difference - of - squares formula $a^{2}-b^{2}=(a + b)(a - b)$ where $a=x$ and $b = 3$). So, $(x + 3)(x - 3)=0$.

Step3: Solve for x

Using the zero - product property (if $ab = 0$, then either $a = 0$ or $b = 0$), we have $x+3 = 0$ or $x - 3=0$. Solving $x+3 = 0$ gives $x=-3$, and solving $x - 3=0$ gives $x = 3$.

Answer:

C. $-3,3$