Задача 3. Найдите корень уравнения \(\dfrac{{x — 105}}{{x + 3}} = — 5.\)
Решение
\(\dfrac{{x — 105}}{{x + 3}} = — 5\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\left\{ {\begin{array}{*{20}{c}}{x + 3 \ne 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\\{x — 105 = — 5x — 15}\end{array}} \right.\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\left\{ {\begin{array}{*{20}{c}}{x \ne — 3\,\,\,}\\{6x = 90}\end{array}} \right.\,\,\,\,\,\,\,\,x = 15.\)
Ответ: 15.