Rational Inequalities II | math4u.vsb.cz

Napsal uživatel michaela.bailova dne Čt, 04/18/2024 - 16:17.

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Question 1:

\frac{(x - 3) (x - 2)}{x^{2} - 4} \leq 0

Answer 1:

x \in (- 2; 2) \cup (2; 3 ⟩

Question 2:

\frac{(x - 4) (x - 2)}{x^{2} + 4} \leq 0

Answer 2:

x \in ⟨ 2; 4 ⟩

Question 3:

\frac{2 x (x - 2) (x + 1)}{x^{2} + 9} \geq 0

Answer 3:

x \in ⟨ - 1; 0 ⟩ \cup ⟨ 2; + \infty)

Question 4:

\frac{- 2 x (x^{3} + 8) (x - 3)}{x^{4} + 16} \leq 0

Answer 4:

x \in ⟨ - 2; 0 ⟩ \cup ⟨ 3; + \infty)

Question 5:

\frac{2 x (x + 2) (3 x^{2} + 6)}{x^{2} - 1} \leq 0

Answer 5:

x \in ⟨ - 2; - 1) \cup ⟨ 0; 1)

Question 6:

\frac{(2 x + 2) (x - 3)}{x^{2} + 1} \leq 0

Answer 6:

x \in ⟨ - 1; 3 ⟩

Question 7:

\frac{(2 x^{2} - 8) (x + 3)}{(x^{2} + 1) (x^{2} + 4)} \geq 0

Answer 7:

x \in ⟨ - 3; - 2 ⟩ \cup ⟨ 2; + \infty)

Question 8:

\frac{(x + 4)}{(x^{3} + 1)} > 0

Answer 8:

(- \infty; - 4) \cup (- 1; + \infty)