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Solve for $x: \frac{4}{x} - \frac{5}{2x + 3} = 3$
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$$\begin{aligned}& 4 (2x + 3) - 5x = 3x (2x + 3) \\ & \Rightarrow 6x^2 + 6x - 12 = 0\end{aligned}$$ or $$\begin{aligned}& x^2 + x - 2 = 0 \\ & \Rightarrow (x - 1) (x + 2) = 0 \\ & \Rightarrow x = 1, x = -2\end{aligned}$$