[tex]x - \frac{ - 6}{x - 3} = \frac{2x}{x - 3} [/tex]
[tex](x - \frac{ - 6}{ x - 3} = \frac{2x}{x - 3} )x - 3[/tex]
[tex] {x}^{2} - 3x - \frac{ - 6(x - 3)}{x - 3} = \frac{2x(x - 3)}{x - 3} [/tex]
[tex] {x}^{2} - 3x - ( - 6) = 2x[/tex]
[tex] {x}^{2} - 3x + 6 = 2x[/tex]
[tex] {x}^{2} - 3x - 2x + 6 = 2x - 2x[/tex]
[tex] {x}^{2} - 5x + 6 = 0 \: \: \: (quadratic form)[/tex]
[tex](x - 3)(x - 2) = 0[/tex]
[tex]Values \: of \: x: \\ x - 3 = 0 \\ x = 3 \\ x - 2 = 0 \\ x = 2[/tex]
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[tex]x - \frac{ - 6}{x - 3} = \frac{2x}{x - 3} [/tex]
[tex](x - \frac{ - 6}{ x - 3} = \frac{2x}{x - 3} )x - 3[/tex]
[tex] {x}^{2} - 3x - \frac{ - 6(x - 3)}{x - 3} = \frac{2x(x - 3)}{x - 3} [/tex]
[tex] {x}^{2} - 3x - ( - 6) = 2x[/tex]
[tex] {x}^{2} - 3x + 6 = 2x[/tex]
[tex] {x}^{2} - 3x - 2x + 6 = 2x - 2x[/tex]
[tex] {x}^{2} - 5x + 6 = 0 \: \: \: (quadratic form)[/tex]
[tex](x - 3)(x - 2) = 0[/tex]
[tex]Values \: of \: x: \\ x - 3 = 0 \\ x = 3 \\ x - 2 = 0 \\ x = 2[/tex]