9\; ,\; \; (x-3)(x+3)>0\; ,\\\\+++(-3)---(3)+++\qquad x\in (-\infty ,-3)\cup (3,+\infty )\\\\3)\; \; \frac{x(x-1)}{3-x}\leq 0\; ,\; \; \frac{x(x-1)}{-(x-3)}\leq 0\; ,\; \; \frac{x(x-1)}{x-3}\geq 0\\\\---[\, 0\, ]+++[\, 1\, ]---(3)+++\qquad x\in [\, 0,1\, ]\cup (3,+\infty )\\\\4)\; \; x^2(5x-4)(x+7)<0\; ,\\\\+++(-7)---(0)---(4/5)+++\\\\x\in (-7,0)\cup (0,\frac{4}{5})" alt="1)\; \; (x-1)(x+9)<0\qquad +++(-9)---(1)+++\\\\x\in (-9,1)\\\\2)\; \; x^2>9\; ,\; \; (x-3)(x+3)>0\; ,\\\\+++(-3)---(3)+++\qquad x\in (-\infty ,-3)\cup (3,+\infty )\\\\3)\; \; \frac{x(x-1)}{3-x}\leq 0\; ,\; \; \frac{x(x-1)}{-(x-3)}\leq 0\; ,\; \; \frac{x(x-1)}{x-3}\geq 0\\\\---[\, 0\, ]+++[\, 1\, ]---(3)+++\qquad x\in [\, 0,1\, ]\cup (3,+\infty )\\\\4)\; \; x^2(5x-4)(x+7)<0\; ,\\\\+++(-7)---(0)---(4/5)+++\\\\x\in (-7,0)\cup (0,\frac{4}{5})" align="absmiddle" class="latex-formula">
![5)\; \; y=\sqrt{\frac{-3x+x^2-4}{9-x^2}}\; \; ,\; \; OOF:\; \; \left \{ {{\frac{-3x+x^2-4}{9-x^2}\geq 0} \atop {9-x^2\ne 0}} \right. \\\\x^2-3x-4=0\; \; \to \; \; x_1=-1\; ,\; x_2=4\; \; (teorema\; Vieta)\\\\9-x^2\ne 0\; \to \; \; x^2\ne 9\; ,\; \; x\ne \pm 3\\\\\frac{x^2-3x-4}{-(x^2-9)}\geq 0\; \; ,\; \; \frac{(x+1)(x-4)}{(x-3)(x+3)}\leq 0\; \; ,\\\\+++(-3)---[\, -1\, ]+++(3)---[\, 4\, ]+++\\\\x\in (-3,-1\, ]\cup (3,4\, ]](https://tex.z-dn.net/?f=5%29%5C%3B%20%5C%3B%20y%3D%5Csqrt%7B%5Cfrac%7B-3x%2Bx%5E2-4%7D%7B9-x%5E2%7D%7D%5C%3B%20%5C%3B%20%2C%5C%3B%20%5C%3B%20OOF%3A%5C%3B%20%5C%3B%20%5Cleft%20%5C%7B%20%7B%7B%5Cfrac%7B-3x%2Bx%5E2-4%7D%7B9-x%5E2%7D%5Cgeq%200%7D%20%5Catop%20%7B9-x%5E2%5Cne%200%7D%7D%20%5Cright.%20%5C%5C%5C%5Cx%5E2-3x-4%3D0%5C%3B%20%5C%3B%20%5Cto%20%5C%3B%20%5C%3B%20x_1%3D-1%5C%3B%20%2C%5C%3B%20x_2%3D4%5C%3B%20%5C%3B%20%28teorema%5C%3B%20Vieta%29%5C%5C%5C%5C9-x%5E2%5Cne%200%5C%3B%20%5Cto%20%5C%3B%20%5C%3B%20x%5E2%5Cne%209%5C%3B%20%2C%5C%3B%20%5C%3B%20x%5Cne%20%5Cpm%203%5C%5C%5C%5C%5Cfrac%7Bx%5E2-3x-4%7D%7B-%28x%5E2-9%29%7D%5Cgeq%200%5C%3B%20%5C%3B%20%2C%5C%3B%20%5C%3B%20%5Cfrac%7B%28x%2B1%29%28x-4%29%7D%7B%28x-3%29%28x%2B3%29%7D%5Cleq%200%5C%3B%20%5C%3B%20%2C%5C%5C%5C%5C%2B%2B%2B%28-3%29---%5B%5C%2C%20-1%5C%2C%20%5D%2B%2B%2B%283%29---%5B%5C%2C%204%5C%2C%20%5D%2B%2B%2B%5C%5C%5C%5Cx%5Cin%20%28-3%2C-1%5C%2C%20%5D%5Ccup%20%283%2C4%5C%2C%20%5D "5)\; \; y=\sqrt{\frac{-3x+x^2-4}{9-x^2}}\; \; ,\; \; OOF:\; \; \left \{ {{\frac{-3x+x^2-4}{9-x^2}\geq 0} \atop {9-x^2\ne 0}} \right. \\\\x^2-3x-4=0\; \; \to \; \; x_1=-1\; ,\; x_2=4\; \; (teorema\; Vieta)\\\\9-x^2\ne 0\; \to \; \; x^2\ne 9\; ,\; \; x\ne \pm 3\\\\\frac{x^2-3x-4}{-(x^2-9)}\geq 0\; \; ,\; \; \frac{(x+1)(x-4)}{(x-3)(x+3)}\leq 0\; \; ,\\\\+++(-3)---[\, -1\, ]+++(3)---[\, 4\, ]+++\\\\x\in (-3,-1\, ]\cup (3,4\, ]")