Question

resolver la siguiente ecuación cuadrática con cualquier método y su procedimiento completo
$\frac{5}{x^{2} -1} -\frac{6}{x + 1} = 3\frac{5}{8}$

Answer 1

Respuesta:

$\frac{5}{x^{2} -1} -\frac{6}{x + 1} = 3\frac{5}{8} \\ \frac{5}{(x-1)(x + 1) } -\frac{6}{x + 1} = \frac{15}{8} \\ ( \frac{1}{x + 1} )( \frac{5}{x-1} -\frac{6}{1} )= \frac{15}{8} \\ \frac{5}{(x - 1)} - 6 = \frac{15}{8} (x + 1) \\ \frac{5 - 6(x - 1)}{x - 1} = \frac{15}{8} (x + 1) \\ \frac{5 - 6x + 6}{x - 1} = \frac{15}{8} (x + 1) \\ \frac{8(5 - 6x + 6)}{15} = (x + 1)(x - 1) \\ \frac{40 - 48x + 48}{15} = {x}^{2} - 1 \\ 40 - 48x + 48 = 15( {x}^{2} - 1) \\ 40 - 48 {x}^{2} + 48 = 15 {x}^{2} - 15 \\ 40 - 48x + 48 - 15 {x}^{2} + 15 = 0 \\ - 15 {x}^{2} - 48x + 103 = 0 \\ x = \frac{ - 24 - \sqrt{2121} }{15} = 1.47 \\ x = \frac{ - 24 + \sqrt{2121} }{15} = - 4.67$