0}} \right.\; \left \{ {{(4-x)(4+x)\geq 0} \atop {3x+1>0}} \right.\; \left \{ {{x\in [-4,4\, ]} \atop {x\in (-\frac{1}{3},+\infty )}} \right. \; \; \Rightarrow \; \; x\in (-\frac{1}{3},4\, ]\\\\Tak\; kak\; \; \sqrt{4-x^2}\geq 0\; \; pri\; \; x\in ODZ\; \; \Rightarrow \; \; log_{0,5}\frac{(x+1)^2}{3x+1}\leq 0\; ,\\\\\frac{(x+1)^2}{3x+1}\geq 1\; ,\; \; \frac{(x+1)^2}{3x+1}-1\geq 0\; ," alt="\sqrt{4-x^2}\cdot log_{0,5}\frac{(x+1)^2}{3x+1}\leq 0\\\\ODZ:\; \; \left \{ {{4-x^2\geq 0} \atop {\frac{(x+1)^2}{3x+1}>0}} \right.\; \left \{ {{(4-x)(4+x)\geq 0} \atop {3x+1>0}} \right.\; \left \{ {{x\in [-4,4\, ]} \atop {x\in (-\frac{1}{3},+\infty )}} \right. \; \; \Rightarrow \; \; x\in (-\frac{1}{3},4\, ]\\\\Tak\; kak\; \; \sqrt{4-x^2}\geq 0\; \; pri\; \; x\in ODZ\; \; \Rightarrow \; \; log_{0,5}\frac{(x+1)^2}{3x+1}\leq 0\; ,\\\\\frac{(x+1)^2}{3x+1}\geq 1\; ,\; \; \frac{(x+1)^2}{3x+1}-1\geq 0\; ," align="absmiddle" class="latex-formula">
![\frac{(x+1)^2-3x-1}{3x+1}\geq 0\; \; ,\; \; \frac{x^2+2x+1-3x-1}{3x+1}\geq 0\; \; ,\; \; \frac{x(x-1)}{3x+1}\geq 0\; ,\\\\znaki:\; \; ---(-\frac{1}{3})+++[\, 0\, ]---[\, 1\, ]+++\\\\x\in (-\frac{1}{3},0\, ]\cup [\, 1,+\infty )\\\\\left \{ {{x\in (-\frac{1}{3},0\, ]\cup [\, 1,+\infty )} \atop {x\in (-\frac{1}{3},4\, ]}} \right. \; \; \; \Rightarrow \; \; \underline {\; x\in (-\frac{1}{3},0\, ]\cup [\, 1,4\, ]\; }](https://tex.z-dn.net/?f=%5Cfrac%7B%28x%2B1%29%5E2-3x-1%7D%7B3x%2B1%7D%5Cgeq%200%5C%3B%20%5C%3B%20%2C%5C%3B%20%5C%3B%20%5Cfrac%7Bx%5E2%2B2x%2B1-3x-1%7D%7B3x%2B1%7D%5Cgeq%200%5C%3B%20%5C%3B%20%2C%5C%3B%20%5C%3B%20%5Cfrac%7Bx%28x-1%29%7D%7B3x%2B1%7D%5Cgeq%200%5C%3B%20%2C%5C%5C%5C%5Cznaki%3A%5C%3B%20%5C%3B%20---%28-%5Cfrac%7B1%7D%7B3%7D%29%2B%2B%2B%5B%5C%2C%200%5C%2C%20%5D---%5B%5C%2C%201%5C%2C%20%5D%2B%2B%2B%5C%5C%5C%5Cx%5Cin%20%28-%5Cfrac%7B1%7D%7B3%7D%2C0%5C%2C%20%5D%5Ccup%20%5B%5C%2C%201%2C%2B%5Cinfty%20%29%5C%5C%5C%5C%5Cleft%20%5C%7B%20%7B%7Bx%5Cin%20%28-%5Cfrac%7B1%7D%7B3%7D%2C0%5C%2C%20%5D%5Ccup%20%5B%5C%2C%201%2C%2B%5Cinfty%20%29%7D%20%5Catop%20%7Bx%5Cin%20%28-%5Cfrac%7B1%7D%7B3%7D%2C4%5C%2C%20%5D%7D%7D%20%5Cright.%20%5C%3B%20%5C%3B%20%5C%3B%20%5CRightarrow%20%5C%3B%20%5C%3B%20%5Cunderline%20%7B%5C%3B%20x%5Cin%20%28-%5Cfrac%7B1%7D%7B3%7D%2C0%5C%2C%20%5D%5Ccup%20%5B%5C%2C%201%2C4%5C%2C%20%5D%5C%3B%20%7D "\frac{(x+1)^2-3x-1}{3x+1}\geq 0\; \; ,\; \; \frac{x^2+2x+1-3x-1}{3x+1}\geq 0\; \; ,\; \; \frac{x(x-1)}{3x+1}\geq 0\; ,\\\\znaki:\; \; ---(-\frac{1}{3})+++[\, 0\, ]---[\, 1\, ]+++\\\\x\in (-\frac{1}{3},0\, ]\cup [\, 1,+\infty )\\\\\left \{ {{x\in (-\frac{1}{3},0\, ]\cup [\, 1,+\infty )} \atop {x\in (-\frac{1}{3},4\, ]}} \right. \; \; \; \Rightarrow \; \; \underline {\; x\in (-\frac{1}{3},0\, ]\cup [\, 1,4\, ]\; }")