Question

solve
$\frac{x}{x - 1} + \frac{x - 1}{x} = 2 \frac{1}{2}$
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Answer 1

Answer:

$\frac{x }{x - 1} + \frac{x - 1}{x} = 2 \frac{1}{2} \\ \\ = > \frac{ {x}^{2} + {(x - 1)}^{2} }{x(x - 1)} = \frac{5}{2} \\ \\ = > \frac{ {x}^{2} + {x}^{2} + 1 - 2x }{ {x}^{2} - x } = \frac{5}{2} \\ \\ = > 2(2 {x}^{2} - 2x + 1) = 5( {x}^{2} - x) \\ = > 4 {x}^{2} - 4x + 2 = 5 {x}^{2} - 5x \\ = > {x}^{2} - x - 2 = 0 \\ = > {x}^{2} + x - 2x - 2 = 0 \\ = > x(x + 1) - 2(x + 1) = 0 \\ = > (x - 2)(x + 1) = 0 \\ = > x = 2 , - 1$

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