The solution set of the inequality $\frac{2x+3}{x-1}<0$ is:

$x ∈ (-\frac{3}{2},1)$

The correct answer is Option (3) → $x ∈ (-\frac{3}{2},1)$

Given inequality: $\frac{2x+3}{x-1} < 0$

Find zeros of numerator and denominator:

Numerator: $2x + 3 = 0 \Rightarrow x = -\frac{3}{2}$

Denominator: $x - 1 = 0 \Rightarrow x = 1$

Critical points: $x = -\frac{3}{2}, 1$

Test intervals:

1. $x < -\frac{3}{2}$: $(2x+3)/(x-1) = (-)/(−) = +$ → not valid

2. $-3/2 < x < 1$: $(+)/(−) = −$ → valid

3. $x > 1$: $(+)/(+) = +$ → not valid

Solution set: $x \in \left(-\frac{3}{2}, 1\right)$