Question

$\frac{x + \frac{5}{2} }{2x - \frac{3}{5} } - \frac{x + 3}{2x + 1} = 0$
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Answer 1

Answer:

$\frac{x + \frac{5}{2} }{2x - \frac{3}{5} } - \frac{x + 3}{2x + 1} = 0 \\ \\ \frac{x + \frac{5}{2} }{2x - \frac{3}{5} } = \frac{x + 3}{2x + 1} \\ \\ \frac{ \frac{2x + 5}{2} }{ \frac {10x - 3}{5} } = \frac{x + 3}{2x + 1} \\ \\ \frac{2x + 5}{2} \times \frac{5}{10x - 3} = \frac{x + 3}{2x + 1} \\ \\ \frac{2x + 5(5)} {10x - 3(2)} = \frac{x + 3}{2x + 1} \\ \\ \frac{10x + 25}{20x - 6} = \frac{x + 3}{2x + 1} \\ \\ \frac{20 { x}^{2} + 60x + 25}{20 {x}^{2} + 54x - 18} = 1 \\ \\ {20 { x}^{2} + 60x + 25} = \\ 20 {x}^{2} + 54x - 18 \\ \\ 6x + 43 \: \\ x = \frac{ - 43}{6}$