Question

Решите квадратные неравенства.

Answer 1

$\frac{x-1}{x-3} \ \textless \ 3\\ \frac{x-1}{x-3} - \frac{3x-9}{x-3} \ \textless \ 0\\ \frac{8-2x}{x-3} \ \textless \ 0\\ ....-...(3)...........+.........(4).....-......\\ x\in(- \infty; 3)U(4;+\infty)$

$\frac{x-2}{x+4} \ \textgreater \ \frac{x+4}{x-2} \\ \frac{(x-2)^2-(x+4)^2}{(x-2)(x+4)} \ \textgreater \ 0\\ \frac{x^2-4x+4-x^2-8x-16}{(x-2)(x+4)} \ \textgreater \ 0\\ \frac{-12x-12}{(x-2)(x+4)} \ \textgreater \ 0\\ ....+......(-4)....-......(-1).....+.....(2).....-......\\ x\in (-\infty;-4)U(-1;2)$

4) _-___(-3)___+_____(2)____-____(4)_____+___
x∈(-∞; -3) U (2; 4)

5) __+_(-3)___-___(1)___+___(2)__-____(4)__+__
x∈(-∞; -3) U (1; 2) U (4; +∞)