\(\frac{6x}{x-2}+\frac{6x}{\left(x-2\right)\left(x-5\right)}=\frac{2x}{x-5}\) (ĐKXĐ: x \(\ne\) 2; x \(\ne\) 5)
\(\Leftrightarrow\) \(\frac{6x\left(x-5\right)}{\left(x-2\right)\left(x-5\right)}+\frac{6x}{\left(x-2\right)\left(x-5\right)}=\frac{2x\left(x-2\right)}{\left(x-2\right)\left(x-5\right)}\)
\(\Leftrightarrow\) 6x(x - 5) + 6x = 2x(x - 2)
\(\Leftrightarrow\) 6x2 - 30x + 6x = 2x2 - 4x
\(\Leftrightarrow\) 6x2 - 2x2 = -4x + 30x - 6x
\(\Leftrightarrow\) 4x2 = 20x
\(\Leftrightarrow\) 4x = 20
\(\Leftrightarrow\) x = 5 (KTMĐK)
Vậy S = \(\varnothing\)
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