Question

مsolve for x
1
$\frac{1}{x + 1} - \frac{3}{5x +1 } = \frac{5}{x + 4}$
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Answer 1

Step-by-step explanation:

$\frac{1}{x + 1} - \frac{3}{5x + 1} = \frac{5}{x + 4} \\ \\ \frac{(5x + 1) - 3(x + 1)}{(x + 1)(5x + 1)} = \frac{5}{x + 4} \\ \\ \frac{5x + 1 - 3x - 3}{(5x {}^{2} + x + 5x + 1)} = \frac{5}{x + 4} \\ \\ \frac{(2x - 2)}{(5x {}^{2} + 6x + 1)} = \frac{5}{x + 4} \\ \\ (2x - 2) \times (x + 4) = 5(5 {x}^{2} + 6x + 1) \\ \\ 2x {}^{2} + 8x - 2x - 8 = 25 {x}^{2} + 30x + 5 \\ \\ 25x {}^{2} - 2 {x}^{2} + 30x - 6x + 5 + 8 = 0 \\ \\ 23{x}^{2} + 24x + 13 = 0$