To solve the rational inequality $\frac{x-1}{x+3} \ge 0$, first identify the zero partition numbers where the numerator or denominator equals zero. The numerator $x-1 = 0$ when $x=1$, and the denominator $x+3 = 0$ when $x=-3$. These zero partition numbers, $1$ and $-3$, divide the number line into three intervals: $(-\infty, -3)$, $(-3, 1)$, and $(1, \infty)$. Testing a value in each interval—such as $-4$, $0$, and $2$—reveals the sign of the quotient. The quotient is positive in $(-\infty, -3)$ and $(1, \infty)$, and negative in $(-3, 1)$. Because the inequality requires the expression to be greater than or equal to zero, the intervals $(-\infty, -3)$ and $(1, \infty)$ are solutions. The partition number $x=-3$ must be excluded with a parenthesis because it makes the denominator zero, yielding an undefined expression. The partition number $x=1$ is included with a bracket because it makes the rational expression zero, which satisfies the $\ge$ condition. Connecting the two valid intervals with the union symbol gives the final solution: $(-\infty, -3) \cup [1, \infty)$.