Question

Решите уравнение:
3/х-3-6/2-х=6

Answer 1

$\frac{3}{x-3} - \frac{6}{2-x} =6\\\\ \frac{3}{x-3}- \frac{6}{2-x} -6=0\\\\ \frac{6-3x-6x+18-30x+6 x^{2} +36}{(x-3)(2-x)}=0\\\\ \frac{6 x^{2} -39x+60}{(x-3)(2-x)}=0$
6x² - 39x + 60 = 0                        x - 3 ≠ 0  ⇒  x ≠ 3         2 - x ≠ 0   ⇒  x ≠ 2
2x² - 13x + 20 = 0
D = (- 13)² - 4 * 2 * 20= 169 - 160 = 9 = 3²
$x_{1}= \frac{13+3}{4}=4\\\\ x_{2}= \frac{13-3}{4} =2,5$