Question

the value of x on solving x/x-1 + x-1/x=2 1/2 will be​

Answer 1

Answer:

Value of x = 2 and -1

Step-by-step explanation:

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

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