Question

If $x-\frac{1}{x-2}=2-\frac{1}{x-2}$ then x is equal to

• A. 1
• B. 2
• C. 3
• D. none of these

Answer 1

The correct option is B 2

Given,

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

$\Rightarrow \frac{x^2-2x-1}{x-2}=\frac{2x-4-1}{x-2}$

$\Rightarrow x^2-2x-1=2x-4-1$(cancelling x-2 on both sides)

$\Rightarrow x^2-2x-1-2x+4+1=0$

$\Rightarrow x^2-4x+4=0$

$\Rightarrow x^2-2x-2x+4=0$

$\Rightarrow x(x-2)-2(x-2)$

$\Rightarrow (x-2)(x-2)$

$\Rightarrow x-2=0$

$\Rightarrow x=2$