[tex] \frac{x}{2x - 3} + \frac{4}{x + 1} = 1\:(x\neq -1,x\neq \frac{3}{2}) \\ \Leftrightarrow \frac{x(x + 1) + 4(2x - 3)}{(2x - 3)(x + 1)} = \frac{(2x - 3)(x + 1)}{(2x - 3)(x + 1)} \\ \Leftrightarrow x(x + 1) + 4(2x - 3) = (2x - 3)(x + 1) \\ \Leftrightarrow {x}^{2} + x + 8x - 12 = 2 {x}^{2} -x - 3 \\ \Leftrightarrow {x}^{2} - 10x + 9 = 0 \\ \Leftrightarrow {x}^{2} - 9x - x + 9 = 0 \\ \Leftrightarrow x(x - 9) - (x - 9) = 0 \\ \Leftrightarrow (x - 9)(x - 1) = 0 \\ \Leftrightarrow x = 1 \: \vee \: x = 9[/tex]
