Question

Помогите решить пожалуйста
1.( 5/x ) - (3/3-x) < 0
2. sin2x+((√3)/2)=0 

Answer 1

$\frac{5}{x}-\frac{3}{3-x}\ \textless \ 0\\\\\frac{5(3-x)-3x}{x(3-x)}\ \textless \ 0\\\\\frac{15-5x-3x}{x(3-x)}\ \textless \ 0\\\\\frac{15-8x}{-x(x-3)}\ \textless \ 0\\\\\frac{-8(x-\frac{15}{8})}{-x(x-3)}\ \textless \ 0\\\\\frac{8(x-\frac{15}{8})}{x(x-3)}\ \textless \ 0\\\\Znaki:\; \; ---(0)+++(\frac{15}{8})---(3)+++\\\\x\in (-\infty,0)U(\frac{15}{8},3)$

$2)sin2x=-\frac{\sqrt3}{2}\\\\2x=(-1)^{n}\cdot (-\frac{\pi}{3})+\pi n=(-1)^{n+1}\cdot \frac{\pi}{3}+\pi n,\; n\in Z\\\\x=(-1)^{n+1}\cdot \frac{\pi}{6}+\frac{\pi n}{2},\; n\in Z$