Question

Помогите пожалуйста решыть пример с обяснениэм
ДАЮ ЛУЧШИЙ ОТВЕТ​

Answer 1

$\displaystyle\bf\\\frac{x^{2} -9x+50}{x^{2} -5x} =\frac{x+1}{x-5} +\frac{x-5}{x} \\\\\\\frac{x^{2} -9x+50}{x(x -5)} -\frac{x+1}{x-5} -\frac{x-5}{x} =0\\\\\\\frac{x^{2} -9x+50-(x+1)\cdot x-(x-5)\cdot(x-5)}{x(x-5)} =0\\\\\\\frac{x^{2} -9x+50-x^{2} -x-x^{2} +10x-25}{x(x-5)} =0\\\\\\\frac{-x^{2} +25}{x(x-5)} =0\\\\\\\frac{x^{2} -25}{x(x-5)} =0\\\\\\\frac{(x-5)(x+5)}{x(x-5)} =0\\\\\\\left \{ {{\left[\begin{array}{ccc}x-5=0\\x+5=0\end{array}\right} \atop {x\neq 0 \ , \ x\neq5 }} \right.$

$\displaystyle\bf\\\left \{ {{\left[\begin{array}{ccc}x=5-neyd\\x=-5\end{array}\right } \atop {x\neq 0 \ , \ x\neq 5}} \right. \\\\\\Otvet:-5$