Задача 17. Найдите корень уравнения \(\dfrac{1}{{3x — 4}} = \dfrac{1}{{4x — 11}}.\)
Решение
\(\dfrac{1}{{3x — 4}} = \dfrac{1}{{4x — 11}}\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\left\{ {\begin{array}{*{20}{c}}{3x — 4 \ne 0,\,\,\,4x — 11 \ne 0}\\{3x — 4 = 4x — 11\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\end{array}} \right.\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\left\{ {\begin{array}{*{20}{c}}{x \ne \dfrac{4}{3},\,\,\,x \ne 2,75}\\{x = 7\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}\end{array}} \right.\,\,\,\,\, \Leftrightarrow \,\,\,\,\,x = 7.\)
Ответ: 7.