1 + \(\frac{x}{x+3}\) = \(\frac{7x}{\left(x-2\right)\left(x+3\right)}\) + \(\frac{2}{x-2}\)
\(\Leftrightarrow\) \(\frac{\left(x-2\right)\left(x+3\right)}{\left(x-2\right)\left(x+3\right)}\) + \(\frac{x\left(x-2\right)}{\left(x-2\right)\left(x+3\right)}\) = \(\frac{7x}{\left(x-2\right)\left(x+3\right)}\) + \(\frac{2\left(x+3\right)}{\left(x-2\right)\left(x+3\right)}\)
\(\Leftrightarrow\) (x - 2)(x + 3) + x(x - 2) = 7x + 2(x + 3)
\(\Leftrightarrow\) (x - 2)(x + 3 + x) = 7x + 2x + 6
\(\Leftrightarrow\) (x - 2)(2x + 3) = 9x + 6
\(\Leftrightarrow\) 2x2 + 3x - 4x - 6 = 9x + 6
\(\Leftrightarrow\) 2x2 + 3x - 4x - 9x = 6 + 6
\(\Leftrightarrow\) 2x2 - 10x = 12
\(\Leftrightarrow\) 2x(x - 5) = 12
\(\Leftrightarrow\) x = 6
Vậy S = {6}
Chúc bạn học tốt! :))
