First slide

Introduction to sets

Question

complete solution set of inequality $\frac{(x + 2) (x + 3)}{(x - 2) (x - 3)} \leq 1$ is

Moderate

A

$(- \infty, 0]$
B

$(- \infty, 0] \cup (2, 3)$
C

$[2, 3]$
D

$(- \infty, 2) \cup (3, \infty)$

Solution

$\begin{array}{l} \frac{(x + 2) (x + 3)}{(x - 2) (x - 3)} \leq 1 \\ \Rightarrow \frac{x^{2} + 5 x + 6}{x^{2} - 5 x + 6} - 1 \leq 0 \\ \Rightarrow \frac{10 x}{(x - 2) (x - 3)} \leq 0 \end{array}$
$x \in (- \infty, 0] \cup (2, 3)$

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