9. \( \frac{x^{2}-6 x+9}{5-4 x-x^{2}} \geqslant 0 \)

1.	9. \( \frac{x^{2}-6 x+9}{5-4 x-x^{2}} \geqslant 0 \)
Answer» \(\frac{x^2 - 6x + 9}{5 - 4x - x^2} \ge 0\) ⇒ \(\frac{(x - 3)^2}{-(x^2 + 4x - 5)} \ge 0\) ⇒ \(\frac{(x - 3)^2}{(x + 5) (x - 1)} \le 0\) ⇒ \((x -3)^2 = 0 \; or\;(x + 5) (x - 1) < 0\) \((\because (x - 3)^2 \ge 0)\) ⇒ \(x = 3 \;or\; -5< x< 1\) ⇒ \(x \in (-5, 1) \cup \{3\}\)

Answer»

\(\frac{x^2 - 6x + 9}{5 - 4x - x^2} \ge 0\)

⇒ \(\frac{(x - 3)^2}{-(x^2 + 4x - 5)} \ge 0\)

⇒ \(\frac{(x - 3)^2}{(x + 5) (x - 1)} \le 0\)

⇒ \((x -3)^2 = 0 \; or\;(x + 5) (x - 1) < 0\) \((\because (x - 3)^2 \ge 0)\)

⇒ \(x = 3 \;or\; -5< x< 1\)

⇒ \(x \in (-5, 1) \cup \{3\}\)

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9. \( \frac{x^{2}-6 x+9}{5-4 x-x^{2}} \geqslant 0 \)

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