Question

Rezolvati in R ecuatia.
..Va rog repede dau coroana
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Answer 1

$\dfrac{x}{x^{2} - 6x + 9} = \dfrac{5x}{x - 3}$

$\dfrac{x}{(x - 3)^{2}} = \dfrac{5x}{x - 3}$

$x - 3 \neq 0 \implies x \neq 3$

$x(x - 3) = 5x(x - 3)^{2} \ \ \Big|:(x-3)$

$x = 5x(x - 3) \iff 5x(x - 3) - x = 0$

$x(5x - 15 - 1) = 0 \iff x(5x - 16) = 0$

$x_{1} = 0$

$5x - 16 = 0 \implies x_{2} = \dfrac{16}{5}$

$S = \Big\{0;\dfrac{16}{5} \Big\}$