Solve the following quadratic equation by factorization, the root is : $-1$ and $1$ $\dfrac{x \, - \, 1}{2x \, + \, 1} \, + \, \dfrac{2x \, + \, 1}{x \, - \, 1} \, = \, \dfrac{5}{2}, \, x \, \neq \, -\dfrac{1}{2}, \, 1$

To solve the equation, let (x - 1)/(2x + 1) be equal to y. The equation then becomes y + 1/y = 5/2, which can be rewritten as 2y^2 - 5y + 2 = 0. Factoring this quadratic equation gives (2y - 1)(y - 2) = 0, meaning y = 1/2 or y = 2. Substituting the original expression back for y = 2 gives (x - 1)/(2x + 1) = 2, which results in x - 1 = 4x + 2 and thus x = -1. For y = 1/2, we get 2x - 2 = 2x + 1, which has no valid solution, so the only root is -1. Therefore, the statement that the roots are -1 and 1 is False.

• Thanks
• Wrong explanation