Question

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

• A. $1$
• B. $2$
• C. $-1$
• D. None of these

Answer 1

The correct option is D None of these

$Givenx-\frac{1}{x-2}=2-\frac{1}{x-2}OptionA\to x=1L.H.S=1-\frac{1}{1-2}=2R.H.S=2-\frac{1}{2-2}\to indeterminate\therefore L.H.S\ne R.H.S\therefore Thisoptionisnotcorrect.OptionB\to x=2\therefore L.H.S=1-\frac{1}{2-2}\to indeterminateR.H.S\to indeterminateasx-2iszero\therefore Thisoptionisalsonottrue.OptionC\to x=3\therefore L.H.S=1-\frac{1}{3-2}=0R.H.S=2-\frac{1}{3-2}=1\therefore L.H.S\ne R.H.S\therefore Thisoptionisnottrue.\therefore OptionDiscorrect.$