Question

solve the equation
$(x + 1 \x - 1) -( x - 1 \x + 1) = 5 \6$
Solve the equation ​

Answer 1

Answer:

$\frac{x + 1}{x - 1} - \frac{x - 1}{x + 1} = \frac{5}{6} \\ \\ = > \frac{(x + 1)(x + 1) - (x - 1)(x - 1)}{(x - 1)(x + 1)} = \frac{5}{6} \\ \\ = > \frac{(x + 1) ^{2} -( {x - 1})^{2} }{ {x}^{2} - {1}^{2} } = \frac{5}{6} \\ \\ = > \frac{ {x}^{2} + 2x + 1 - ( {x}^{2} - 2x + 1) }{ {x}^{2} - 1} = \frac{5}{6} \\ \\ = > \frac{ {x}^{2} + 2x + 1 - {x}^{2} + 2x - 1 }{ {x}^{2} - 1} = \frac{5}{6} \\ \\ = > \frac{4x}{ {x}^{2} - 1 } = \frac{5}{6} \\ \\ = > {5x}^{2} - 5 = 24x \\ \\ = > {5x}^{2} - 5 - 24x = 0 \\ \\ = > {5x}^{2} - 24x - 5 = 0 \\ \\ = > {5x}^{2} - (25 - 1)x - 5 = 0 \\ \\ = > {5x}^{2} - 25x + x - 5 = 0 \\ \\ = > 5x( x - 5) + 1(x - 5) = 0 \\ \\ = > (5x + 1)(x - 5) = 0 \\ \\ either \: 5x + 1 = 0 \\ \\ = > x = \frac{ - 1}{5} \\ \\ or \: x - 5 = 0 \\ \\ = > x = 5$

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