Rational expression

\frac{1}{4 x + 1} - \frac{1}{3} + \frac{1}{2 x - 3}

\frac{3}{3} \frac{2 x - 3}{2 x - 3} \cdot \frac{1}{4 x + 1} - \frac{4 x + 1}{4 x + 1} \frac{2 x - 3}{2 x - 3} \cdot \frac{1}{3} + \frac{4 x + 1}{4 x + 1} \frac{3}{3} \cdot \frac{1}{2 x - 3}

\frac{3 (2 x - 3)}{3 (4 x + 1) (2 x - 3)} - \frac{(4 x + 1) (2 x - 3)}{3 (4 x + 1) (2 x - 3)} + \frac{3 (4 x + 1)}{3 (4 x + 1) (2 x - 3)}

\frac{6 x - 9}{3 (4 x + 1) (2 x - 3)} - \frac{8 x^{2} - 12 x + 2 x - 3}{3 (4 x + 1) (2 x - 3)} + \frac{12 x + 3}{3 (4 x + 1) (2 x - 3)}

\frac{6 x - 9}{3 (4 x + 1) (2 x - 3)} - \frac{8 x^{2} - 10 x - 3}{3 (4 x + 1) (2 x - 3)} + \frac{12 x + 3}{3 (4 x + 1) (2 x - 3)}

\frac{6 x - 9 - (8 x^{2} - 10 x - 3) + 12 x + 3}{3 (4 x + 1) (2 x - 3)}

\frac{6 x - 9 - 8 x^{2} + 10 x + 3 + 12 x + 3}{3 (4 x + 1) (2 x - 3)}

\frac{- 8 x^{2} + 28 x - 3}{3 (4 x + 1) (2 x - 3)}

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