Question

The equation x - 2/x-1=1-2/x-1 has roots​

Answer 1

GIVEN :

The equation $x-\frac{2}{x-1}=1-\frac{2}{x-1}$

TO FIND :

The roots for the given equation.

SOLUTION :

Given equation is $x-\frac{2}{x-1}=1-\frac{2}{x-1}$ for $x-1\neq 0$

To find the roots for the given equation :

Since the given equation $x-\frac{2}{x-1}=1-\frac{2}{x-1}$ is true for the value $x\neq 1$

Now solving the equation $x-\frac{2}{x-1}=1-\frac{2}{x-1}$  as below :

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

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

$x=1+0$

x=1

∴ x=1 which is not possible ( ∵ $x\neq 1$ )

∴  the given equation has no roots.