Question

solve x/x-1 +x-1/x=5/2

Answer 1

x = - 1  or  2  if  x/x-1 +x-1/x=5/2

Step-by-step explanation:

x/(x - 1)  + (x - 1)/x  = 5/2

Multiplying both sides by 2x(x-1)

=> 2x²  + 2(x - 1)² = 5x(x-1)

=> 2x² + 2(x² - 2x + 1) = 5x² - 5x

=> 2x² + 2x² - 4x + 2 = 5x² - 5x

=> 4x² - 4x + 2 = 5x² - 5x

=> x² - x - 2 = 0

=>x² - 2x + x - 2 = 0

=> x(x - 2) + 1(x - 2) = 0

=>(x + 1)(x - 2) = 0

=> x = - 1  or  2

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Answer 2

Answer:

$\huge\bf{Answer..}$

$\frac{x}{x - 1} + \frac{x - 1}{x} = \frac{5}{2} \\ \implies \: \: \: \frac{x {}^{2} + (x - 1) {}^{2} }{x(x - 1)} = \frac{5}{2} \\ \implies \: \: \: \frac{x {}^{2} + x {}^{2} - 2x + 1 }{x {}^{2} - x } = \frac{5}{2} \\ \implies \: \: \: \frac{2x {}^{2} - 2x + 1}{x {}^{2} - x } = \frac{5}{2} \\ \implies \: \: \: 5(x {}^{2} - x) = 2(2x {}^{2} - 2x + 1) \\ \implies \: \: \: 5x {}^{2} - 5x = 4x {}^{2} - 4x + 2 \\ \implies \: \: \: 5x {}^{2} - 5x - 4x {}^{2} + 4x - 2 = 0 \\ \implies \: \: \: x {}^{2} - x - 2 = 0 \\ \implies \: \: \: x {}^{2} - 2x + x - 2 = 0 \\ \implies \: \: \: x(x - 2) + 1(x - 2) = 0 \\ \implies \: \: \: (x + 1)(x - 2) = 0 \\ \implies \: \: \: x + 1 = 0 \\ So,\: \: \: x = - 1 \\ Again, \: \: \: x - 2 = 0 \\ So \: \: \: x = 2$

So the solution is both -1 &

2

Hope it helps you ❤❤❤