(9-x^2)/(x^2-x-2)>= 0

الحلّ

\frac{9 - x ^{2}}{x ^{2} - x - 2} \geq 0

- 3 \leq x < - 1 or 2 < x \leq 3

تدوين الفاصل الزمني

[- 3, - 1) \cup (2, 3]

خطوات الحلّ

\frac{9 - x ^{2}}{x ^{2} - x - 2} \geq 0

\frac{9 - x ^{2}}{x ^{2} - x - 2}

حلل إلى عوامل:

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

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

Multiply both sides by

- 1

(reverse the inequality)

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

بسّط

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

ميّز المقاطع المختلفة

- 3 \leq x < - 1 or 2 < x \leq 3

e^{2 iπ}

3 (- 2 x - 7) > 9

6 x - \frac{2}{3} x^{2} = 3

x^{2} - 3 x - 18 \leq 0