Answer
False: solution sets are different.
Work Step by Step
For $(x+3)(x-1)\geq 0$, we need to find the values of $x$ that, when multiplied, yield a positive result. According to the number lines drawn, this results in the interval $(-∞,-3]$U$[1,∞)$. In the case of $\frac{x+3}{x-1}\geq0$, however: $$x+3 \geq 0; x\neq 1$$ $$x\geq -3; x\neq1$$ which results in the interval $(-∞, -3]$U$(1,∞)$.
