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Ответ:

[tex] \frac{ {x}^{2} }{x - 6} = \frac{4x}{x - 6} \\ \\ {x}^{2} = 4x \\ x - 6≠0 \\ \\ x(x - 4) = 0 \\ x≠6 \\ \\ x1 = 0 \\ x2 = 4 \\ x≠6[/tex]

Ответ:

[tex]x \in \: \{0 ;\: 4 \}\\ [/tex]

Объяснение:

[tex] \frac{{x}^{2} }{x - 6} = \frac{4x}{x - 6} \\ \frac{{x}^{2} }{x - 6} - \frac{4x}{x - 6} = 0\\ \begin{cases} {x}^{2} - 4x = 0 \\ x - 6 \neq0 \end{cases} \: {< = > }\begin{cases} {x}(x - 4) = 0 \\ x \neq6 \end{cases} \: \\ \begin{cases} \left[ \begin{array}{l} x = 0 \\ x - 4 = 0 \end{array} \right.\\ x \neq6 \end{cases} \: {< = > } \begin{cases} \left[ \begin{array}{l} x = 0 \\ x = 4 \end{array} \right.\\ x \neq6 \end{cases} \: \\ {< = > }\left[ \begin{array}{l} x = 0 \\ x = 4 \end{array} \right. \: \: {= > }x \in \: \{0 ;\: 4 \}\\ [/tex]