Question

Пацаны(девчёнки) выручайте пж Дробные уравнения решите полностью плиз (x)/(x-2)+(x^(2))/(2x-9)=0

Answer 1

x(2x-9)+x^(2)(x-2)=0

x^(3)-9x=0

x(x^(2)-9)=0

x=0

x=3

x=-3

Answer 2

$\frac{x}{x-2}+\frac{x^{2}}{2x-9}=0\\\\\frac{x(2x-9)+x^{2}(x-2) }{(x-2)(2x-9)}=0\\\\\frac{2x^{2}-9x+x^{3}-2x^{2}}{(x-2)(2x-9)}=0\\\\\frac{x^{3}-9x }{(x-2)(2x-9)}=0\\\\\left \{ {{x^{3}-9x=0 } \atop {x-2\neq 0;2x-9\neq 0 }} \right. \\\\\left \{ {{x(x^{2}-9)=0 } \atop {x\neq2,x\neq4,5}} \right.\\\\x(x^{2}-9)=0\\\\x(x-3)(x+3)=0\\\\\\\left[\begin{array}{ccc}x_{1}=0 \\x-3=0\\x+3=0\end{array}\right\\\\\\\left[\begin{array}{ccc}x_{1}=0 \\x_{2}=3 \\x_{3}=-3 \end{array}\right$

Ответ : - 3 ; 0 ; 3