Question

The value of x on solving x/x-1+ x-1/x= 5/2​

Answer 1

$\huge\star\:\:{\orange{\underline{\pink{\mathbf{Answer}}}}}$

$\frac{x}{x - 1} + \frac{x - 1}{x} = \frac{5}{2}$

$\frac{ {x}^{2} + {(x - 1)}^{2} }{ {x}^{2} } = \frac{5}{2}$

$2 {x}^{2} + 2 {x}^{2} - 2 - 4x = 5 {x}^{2}$

$4 {x}^{2} - 2 - 4x - 5 {x}^{2}$

$- {x}^{2} - 4x - 2 = 0$

$- {x}^{2} - 2x - 2x - 2 = 0$

Answer 2

$\huge\underbrace\mathfrak\pink{Answer:-}$

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

x²+(x-1)²/ x(x-1) = 5/2

x²+x²+2x+1/x(x-1)=5/2

2x²+2x+1/x²-x=5/2

2(2x²+2x+1)=5(x²-x)

4x²+4x+2=5x²-5

5x²-4x²+4x=-5-2

x²+4x=-7