The equation $$x - \frac{2}{{x - 1}} = 1 - \frac{2}{{x - 1}}\,$$ has
A.
no root
B.
one root
C.
two equal roots
D.
infinitely many roots
Answer :
no root
Solution :
Given equation is $$x - \frac{2}{{x - 1}} = 1 - \frac{2}{{x - 1}}$$
Clearly $$x \ne 1$$ for the given eqn. to be defined. If $$x - 1 \ne 0,$$ we can cancel the common term $$\frac{{ - 2}}{{x - 1}}$$ on both sides to get $$x = 1,$$ but it is not possible. So given eqn. has no roots.
∴ $${\text{(A)}}$$ is the correct answer.
Releted MCQ Question on Algebra >> Quadratic Equation
Releted Question 1
If $$\ell ,m,n$$ are real, $$\ell \ne m,$$ then the roots by the equation: $$\left( {\ell - m} \right){x^2} - 5\left( {\ell + m} \right)x - 2\left( {\ell - m} \right) = 0$$ are