The roots of equation \(x - \frac{2}{{x - 1}} = 1 - \frac{2}{{x - 1}}\) is
Practice this Quadratic Equation question from Engineering Entrance Exam.
Question Details
Mathematics
Quadratic Equation
Engineering Entrance Exam
Question
The roots of equation \(x - \frac{2}{{x - 1}} = 1 - \frac{2}{{x - 1}}\) is
Solution
Consider the given equation
\(x - \frac{2}{{x - 1}} = 1 - \frac{2}{{x - 1}}\)
By taking L.C.M, we get
\(\frac{{x(x - 1) - 2}}{{x - 1}} = \frac{{x - 1 - 2}}{{x - 1}}\)
\( \Rightarrow x(x - 1) - 2 = x - 3\)
\( \Rightarrow {x^2} - x - 2 = x - 3\)
\( \Rightarrow {x^2} - 2x + 1 = 0\)
\( \Rightarrow {(x - 1)^2} = 0\)
\( \Rightarrow x = 1,1\)
Thus, the given equation has two roots.