Rational Inequalities II | math4u.vsb.cz

Submitted by michaela.bailova on Thu, 04/18/2024 - 16:17

Project ID:

7200020079

Accepted:

SubArea:

Rational equations and inequalities

Type:

Layout:

Question:

Every pair you are looking for is an inequality and its solution.

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)