0} \atop {\frac{x}{x+1}\leq 0}} \right. \\\\a)\; \; x^2+3x+2>0\; \; ,\; \; x_1=-1\; ,\; x_2=-2\\\\(x+1)(x+2)>0\; \; \; \; \; +++(-2)---(-1)+++\\\\x\in (-\infty ,-2)\cup (-1,+\infty )\\\\b)\; \; \frac{x}{x+1}\leq 0\; \; \; \; \; +++[-1\, ]---[\, 0\, ]+++\\\\x\in [-1,0\, ]\\\\c)\; \; \left \{ {{x\in (-\infty ,-2)\cup (-1,+\infty )} \atop {x\in [-1,0\, ]}} \right. \; \; \Rightarrow \; \; x\in (-1,0\, ]" alt="\left \{ {{x^2+3x+2>0} \atop {\frac{x}{x+1}\leq 0}} \right. \\\\a)\; \; x^2+3x+2>0\; \; ,\; \; x_1=-1\; ,\; x_2=-2\\\\(x+1)(x+2)>0\; \; \; \; \; +++(-2)---(-1)+++\\\\x\in (-\infty ,-2)\cup (-1,+\infty )\\\\b)\; \; \frac{x}{x+1}\leq 0\; \; \; \; \; +++[-1\, ]---[\, 0\, ]+++\\\\x\in [-1,0\, ]\\\\c)\; \; \left \{ {{x\in (-\infty ,-2)\cup (-1,+\infty )} \atop {x\in [-1,0\, ]}} \right. \; \; \Rightarrow \; \; x\in (-1,0\, ]" align="absmiddle" class="latex-formula">