complete solution set of inequality (x+2)(x+3)(x−2)(x−3)≤1 is

(x+2)(x+3)(x−2)(x−3)≤1⇒ x2+5x+6x2−5x+6−1≤0⇒ 10x(x−2)(x−3)≤0x∈(−∞,0]∪(2,3)

complete solution set of inequality (x+2)(x+3)(x−2)(x−3)≤1 is

(x+2)(x+3)(x−2)(x−3)≤1⇒ x2+5x+6x2−5x+6−1≤0⇒ 10x(x−2)(x−3)≤0x∈(−∞,0]∪(2,3)

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

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$(- \infty, 0]$

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

$[2, 3]$

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

answer is B.

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